Q. 22

# Evaluate the following integrals

Let

Let

Let x=tanθ

θ=tan-1x

=sin-1 (2sinθcosθ)

=sin-1 (sin2θ)

Hence f(x)=2θ

=2tan-1x

Hence

Using integration by parts, we get

-(1)

Let

Let 1+x2=t

2x dx=dt.

Also, when x=0, t=1

and when x=1, t=2

Hence,

–(2)

Substituting value of (2) in (1), we get

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