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Question Number 128245 by mnjuly1970 last updated on 05/Jan/21

$$nicecalculus...$$$$provethat::{\int }_0^{\frac{\pi }{4}}xcot\left(x\right)dx=\frac{1}{2}(G+\frac{\pi }{4}log\left(2\right))$$

Answered by Dwaipayan Shikari last updated on 05/Jan/21

$${\int }_0^{\frac{\pi }{4}}xcotxdx={\left[xlog\left(sinx\right)\right]}_0^{\frac{\pi }{4}}-{\int }_0^{\frac{\pi }{4}}log\left(sinx\right)dx$$$$=-\frac{\pi }{8}log\left(2\right)+\frac{\pi }{4}log\left(2\right)+\frac{G}{2}log\left(2\right)\left(Hasbeenprovedearliar\right)$$$$=\frac{\pi }{8}log\left(2\right)+\frac{G}{2}log\left(2\right)$$$$Q128244$$

Commented by mnjuly1970 last updated on 05/Jan/21

$$gratefulmrpayan...mercey...$$

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