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Evaluate: intcosecxlog(cot (x/2))dx...

Evaluate: `intcosecxlog(cot (x/2))dx`

Text Solution

Verified by Experts

The correct Answer is:
`sinx log("tan"(x)/(2))-x+C`
`int underset(II)(cos)x log(underset(I)("tan")(x)/(2))dx`
`=log("tan"(x)/(2))sinx-int(1)/("tan"(x)/(2))"sec"^(2)(x)/(2)xx(1)/(2)sinx dx +C " " "(Integrating by parts)" `
`=sinx log("tan"(x)/(2))-int(1)/(2"sin"(x)/(2)"cos"(x)/(2))sinxdx+C `
`=sinx log("tan"(x)/(2))-int dx+C`
`=sinx log("tan"(x)/(2))-x+C`
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