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Evaluate: int("log"(tan(x/2)))/(sinx)dx...

Evaluate: `int("log"(tan(x/2)))/(sinx)dx`

Text Solution

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`(d)/(dx)[log("tan"(x)/(2))]=((1)/(2)"sec"^(2)(x)/(2))/("tan"(x)/(2))=(1)/(sinx)`
Now `int(log("tan"(x)/(2)))/(sinx)dx=intlog("tan"(x)/(2))(d)/(dx)[log("tan"(x)/(2))]dx`
`=([log("tan"(x)/(2))]^(2))/(2) +C`
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