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Question Number 123255 by mnjuly1970 last updated on 24/Nov/20

$$\ast \ast \ast nicecalculus\ast \ast \ast$$$$evaluate::$$$$\mathrm{\Phi }={\int }_0^{\frac{\pi }{2}}{log}^3\left(tan\left(x\right)\right)dx=?$$

Answered by Dwaipayan Shikari last updated on 24/Nov/20

$${\int }_0^{\frac{\pi }{2}}{log}^3\left(tanx\right)dx=I$$$$={\int }_0^{\frac{\pi }{2}}{log}^3\left(cotx\right)={\int }_0^{\frac{\pi }{2}}-{log}^3\left(tanx\right)=I$$$$2I=0\Rightarrow I=0$$

Commented by mnjuly1970 last updated on 24/Nov/20

$$thankyou...$$

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