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Category: Integration

advanced-calculus-evaluate-Im-0-pi-2-li-2-sin-x-li-2-csc-x-dx-

Question Number 136060 by mnjuly1970 last updated on 18/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\mathrm{Im}\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {li}_{\mathrm{2}} \left({sin}\left({x}\right)\right)+{li}_{\mathrm{2}} \left({csc}\left({x}\right)\right){dx}\right) \\ $$$$ \\ $$ Answered by mindispower…

sin-3-x-cosx-dx-

Question Number 70482 by Mikaell last updated on 04/Oct/19 $$\int\frac{{sin}^{\mathrm{3}} {x}}{\:\sqrt{{cosx}}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 04/Oct/19 $${u}={cosx}\Rightarrow{du}=−{sinxdx} \\ $$$${sin}^{\mathrm{3}} {x}={sinxsin}^{\mathrm{2}} {x}={sinx}\left(\mathrm{1}−{cos}^{\mathrm{2}}…

n-n-1-f-x-dx-n-N-where-f-x-i-0-n-1-x-i-Can-this-be-integrated-with-evaluating-the-product-

Question Number 4900 by prakash jain last updated on 19/Mar/16 $$\int_{{n}} ^{\:{n}+\mathrm{1}} {f}\left({x}\right)\mathrm{d}{x},\:{n}\in\mathbb{N} \\ $$$${where}\:{f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}+\mathrm{1}} {\prod}}\left({x}−{i}\right) \\ $$$$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{integrated}\:\mathrm{with}\:\mathrm{evaluating}\:\mathrm{the} \\ $$$$\mathrm{product}? \\ $$ Commented by…