Let u =5arctan(1/x), dv dx

Let u = 5 arctan(1/x), dv = dx

du

=

51

+

1 (1/x)2

?

-1 x2

dx

=

5

-dx x2 + 1

,

v

=

x.

Then

3 1

5

arctan

1 x

dx

=

x ? 5 arctan

1 x

3

+

1

3 5x dx 1 x2 + 1

5

= 5 36 - 5 ? 4 + 2

ln(x2 + 1)

3 1

5 3 5 5

=

6

-

4

+

(ln 2

4

-

ln

2)

5 3 5 5 4

= 6 - 4 + 2 ln 2

5 3 5 5

=

6

-

4

+ ln 2 2

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