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Prove that int(0)^(tan^(-1)x)/x dx=1/2in...

Prove that `int_(0)^(tan^(-1)x)/x dx=1/2int_(0)^((pi)/2)x/(sinx)dx`.

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`I=int_(0)^(1)(tan^(-1)x)/x dx`
Putting `x=tan theta`
`:.dx=sec^(2)theta d theta`
`:.I=int_(0)^(pi//4) (theta)/(tan theta).sec^(2) theta d theta`
`=int_(0)^(pi//4)(2theta)/(sin 2theta)d theta`
Putting `2theta=t, ,.2d theta=dt`,
`:. I=int_(0)^(pi//2)t/(sint) . (dt)/2`
`=1/2int_(0)^(pi//2)x/(sinx)dx`
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