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Evaluate int(0)^(1)(tan^(-1)x)/((1+x^(2)...

Evaluate `int_(0)^(1)(tan^(-1)x)/((1+x^(2)))dx`

Text Solution

Verified by Experts

`int_(1)^(3)("tan"^(-1)x/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/x)dx`
`=int_(-1)^(0)("tan"^(-1)x/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/x)dx`
`+int_(0)^(3)("tan"^(-1)x/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/x)dx`
`int_(-1)^(0)-(pi)/2 dx+int_(0)^(3)(pi)/2 dx`
`=[-(pi)/2 x]_(-1)^(0)+[(pi)/2x]_(0)^(3)`
`=2pi`
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