Integration of (3 cos x 2)/(sinx 2 cosx 3)

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Integration of (3 cos x 2)/(sinx 2 cosx 3)

If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *. and *. are unblocked. Here is a very bizarre way to do this. I'm not claiming it's easier, but I just wanted to mention it because it's a little counterintuitive. Let $\theta$ be an angle such that $$\cos \theta = \frac{1}{\sqrt{5}}, \quad \sin \theta = \frac{2}{\sqrt{5}}.$$ Then $$\sin x + 2 \cos x = \sqrt{5} \left(\cos \theta \sin x + \sin \theta \cos x \right) = \sqrt{5} \sin(x + \theta),$$ and $$\int (\sin x + 2 \cos x)^3 \, dx = 5 \sqrt{5} \int \sin^3 (x + \theta) \, dx = 5 \sqrt{5} \int \left(1 - \cos^2 (x + \theta)\right) \sin (x + \theta) \, dx.$$ Now letting $u = \cos (x + \theta)$, $du = -\sin(x + \theta) \, dx$, we obtain $$5 \sqrt{5} \int u^2 - 1\, du = 5 \sqrt{5} \left( \frac{u^3}{3} - u \right) = 5 \sqrt{5} \left( \frac{\cos^3 (x + \theta)}{3} - \cos (x + \theta)\right) + C.$$ We can substitute $\theta$ back into the expression; e.g., $$\frac{1}{3} (\cos x - 2 \sin x)^3 - 5 (\cos x - 2 \sin x) + C.$$ Gerd Altmann/Pixabay If you're trying to figure out what x squared plus x squared equals, you may wonder why there are letters in a math problem. That's because, in the case of an equation like this, x can be whatever you want it to be. To find out what x squared plus x squared equals, you have to multiply x times itself. Then you add that number to itself to get your final answer.Examples of X Squared Plus X Squared Here are some examples of that equation to make it easier to understand. If x equals 2, then x squared, or x times itself, equals 4. Add four to itself, and you get 8. Therefore, 2 squared plus 2 squared equals 8. To use another example, let's see what happens when x equals 3. In that case, x squared equals 9. Then, 9 plus 9 equals 18. The beauty of this equation is that x can equal anything, and you can solve it using whatever value you want for x. Math that Uses Letters We call mathematics that uses letters to take the place of different values algebra. Algebra uses symbols in most cases, letters to represent quantities that don't necessarily have the same value all the time. These quantities are called variables, and you can figure out what those variables mean when you use algebra. Equations are like sentences that explain the relationships between numbers and variables. You figure out what the variables in an equation are by solving it. When you solve an equation in algebra, you break it down to its simplest form and discover what the variables mean. A Brief History of Algebra Since ancient times, mathematicians have worked with unknown variables in different ways. Islamic scholars began to give the science of working with variables a name. They called this type of math the "science of restoration and balancing," and the Arabic word for "restoration," or "al-jabru," became the root word for the word "algebra." As mathematicians in the Middle Ages experimented with the principles of algebra, they realized they could solve equations for two- and three-dimensional items, which led to even more discoveries of what algebra could do. Modern scholars have found even more complex equations that algebra can solve. Algebra in Everyday Life You may have heard people say that you'll never use algebra in your everyday life, but you'd be surprised at how often you use algebra. Algebra comes in handy when you're trying to figure out how much a group of items costs per item. When you're trying to figure out how to split a restaurant bill or how much gas you can buy for a certain amount. You can use algebra to figure out the dimensions of a room or even as you make up your shopping list. Algebra is a versatile form of math that you use more often than you might think and, sometimes, you don't even realize that you're solving math problems. Why It's Important to Learn Algebra Learning algebra is important for more than just solving equations. Educators consider algebra the gateway to higher forms of math, so if you or your child wants to explore a career in science or technology, algebra can unlock so many more new ideas. Algebra can also help students with critical thinking and logic skills. Using algebra is like exercise that helps make your brain stronger. Putting algebra to use in your everyday life can help you in so many ways. MORE FROM This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more \bold{\mathrm{Basic}} \bold{\alpha\beta\gamma} \bold{\mathrm{AB\Gamma}} \bold{\sin\cos} \bold{\ge\div\rightarrow} \bold{\overline{x}\space\mathbb{C}\forall} \bold{\sum\space\int\space\product} \bold{\begin{pmatrix}\square&\square\\\square&\square\end{pmatrix}} \bold{H_{2}O} \square^{2} x^{\square} \sqrt{\square} throot[\msquare]{\square} \frac{\msquare}{\msquare} \log_{\msquare} \pi \theta \infty \int \frac{d}{dx} \ge \le \cdot \div x^{\circ} (\square) |\square| (f\:\circ\:g) f(x) \ln e^{\square} \left(\square\right)^{'} \frac{\partial}{\partial x} \int_{\msquare}^{\msquare} \lim \sum \sin \cos \tan \cot \csc \sec \alpha \beta \gamma \delta \zeta \eta \theta \iota \kappa \lambda \mu u \xi \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega A B \Gamma \Delta E Z H \Theta K \Lambda M N \Xi \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \sin \cos \tan \cot \sec \csc \sinh \cosh \tanh \coth \sech \arcsin \arccos \arctan \arccot \arcsec \arccsc \arcsinh \arccosh \arctanh \arccoth \arcsech \begin{cases}\square\\\square\end{cases} \begin{cases}\square\\\square\\\square\end{cases} = e \div \cdot \times < > \le \ge (\square) [\square] \:\longdivision{} \times \twostack{}{} + \twostack{}{} - \twostack{}{} \square! x^{\circ} \rightarrow \lfloor\square\rfloor \lceil\square\rceil \overline{\square} \vec{\square} \in \forall otin \exist \mathbb{R} \mathbb{C} \mathbb{N} \mathbb{Z} \emptyset \vee \wedge eg \oplus \cap \cup \square^{c} \subset \subsete \superset \supersete \int \int\int \int\int\int \int_{\square}^{\square} \int_{\square}^{\square}\int_{\square}^{\square} \int_{\square}^{\square}\int_{\square}^{\square}\int_{\square}^{\square} \sum \prod \lim \lim _{x\to \infty } \lim _{x\to 0+} \lim _{x\to 0-} \frac{d}{dx} \frac{d^2}{dx^2} \left(\square\right)^{'} \left(\square\right)^{''} \frac{\partial}{\partial x} (2\times2) (2\times3) (3\times3) (3\times2) (4\times2) (4\times3) (4\times4) (3\times4) (2\times4) (5\times5) (1\times2) (1\times3) (1\times4) (1\times5) (1\times6) (2\times1) (3\times1) (4\times1) (5\times1) (6\times1) (7\times1) \mathrm{Radians} \mathrm{Degrees} \square! ( ) % \mathrm{clear} \arcsin \sin \sqrt{\square} 7 8 9 \div \arccos \cos \ln 4 5 6 \times \arctan \tan \log 1 2 3 - \pi e x^{\square} 0 . \bold{=} + \mathrm{simplify} \mathrm{solve\:for} \mathrm{inverse} \mathrm{tangent} \mathrm{line} See All area asymptotes critical points derivative domain eigenvalues eigenvectors expand extreme points factor implicit derivative inflection points intercepts inverse laplace inverse laplace partial fractions range slope simplify solve for tangent taylor vertex geometric test alternating test telescoping test pseries test root test Related ? Graph ? Number Line ? Similar ? Examples ? Our online expert tutors can answer this problem Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us! In partnership with You are being redirected to Course Hero I want to submit the same problem to Course Hero Examples step-by-step \int (2 sin x - 3 cos x)dx en Feedback Updated: 05/02/2021 by Computer Hope X may refer to any of the following: 1. In general, an x is used to represent a generic variable. For example, you may see Computer Hope and other companies write Microsoft Windows 3.x. In this case, the "x" can be replaced with any valid digit. For instance, it may represent the "1" in Windows 3.1 or the "11" in Windows 3.11. 2. When referring to a computer CD drive, an X refers to the transfer speed. For example, the original 1X CD-ROM had a speed of 153,600 BPS, and a 24X CD-ROM has a BPS of 3,686,400 or 153,600 x 24. The higher the number, the faster that data is going to be read from the CD drive. See the CD-ROM definition for further information about transfer speeds. What does the x stand for on 32x? CD-ROM help and support. 3. Formerly Google X, X is a subsidiary of the Alphabet conglomerate. See the X company page for further information. 4. In mathematics, an x may be used to represent a times sign. For example, 4 x 4 = 16. The times sign may also be represented as an interpunct (?) or an asterisk (*). See our multiply page for further information. 5. When shown in the top-right corner of a window, the X is a button used to close a window. 6. X is a service found on some IRC networks that allows users to manage the chat rooms, called channels, that they have access to view. 7. Abbreviation for X Window System. See the x command page for further information about this command. 8. X is a key used with the keyboard shortcuts Alt+X, Command+X, and Ctrl+X. 9. In chat, 'x' or 'X' is a way of representing a kiss. For example, "xoxo" is kiss, hug, kiss, and hug. 10. With regular expressions, "x" is a regular expression flag that allows spaces and comments. 11. With Microsoft Excel and other spreadsheet programs, "X" is the twenty-fourth column of a spreadsheet. To reference the first cell in the column, you'd use "X1." 12. In the phonetic alphabet, "X" is often pronounced as "x-ray." 13. X is the twenty-fourth letter of the English alphabet. The letter "X" comes after "W" and is followed by the letter "Y." To create a capitalized "X" press the Shift key and X at the same time. On a U.S. QWERTY keyboard, the "X" key is on the bottom row, to the right of "Z" and left of the "C" key. See our keyboard page for a visual example of all keyboard keys. Tip In ASCII the uppercase "X" is "088" in decimal (01011000 in binary). The lowercase "x" is "120" in decimal (01111000 in binary). Related information CD terms, Chat terms, Letter, x86

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