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Category: Integration

dx-a-bcosx-2-

Question Number 116999 by TANMAY PANACEA last updated on 08/Oct/20 $$\int\frac{{dx}}{\left({a}+{bcosx}\right)^{\mathrm{2}} } \\ $$ Answered by Olaf last updated on 08/Oct/20 $$\mathrm{I}\left({x}\right)\:=\:\int\frac{{dx}}{\left({a}+{b}\frac{{e}^{{ix}} +{e}^{−{ix}} }{\mathrm{2}}\right)^{\mathrm{2}} }…

x-1-x-1-3-dx-

Question Number 51419 by Tawa1 last updated on 26/Dec/18 $$\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\mathrm{dx} \\ $$ Answered by Smail last updated on 27/Dec/18 $${let}\:{u}=\sqrt[{\mathrm{6}}]{{x}}\Rightarrow\mathrm{6}{u}^{\mathrm{5}} {du}={dx} \\ $$$${A}=\int\frac{\sqrt{{x}}}{\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}}}{dx}=\int\frac{{u}^{\mathrm{3}} }{\mathrm{1}+{u}^{\mathrm{2}} }\left(\mathrm{6}{u}^{\mathrm{5}}…

Question-116903

Question Number 116903 by mnjuly1970 last updated on 07/Oct/20 Answered by mathmax by abdo last updated on 07/Oct/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{acosx}\right)}{\mathrm{cosx}}\:\mathrm{dx}\:\:\left(\mathrm{here}\:\mathrm{a}=\mathrm{sin}\alpha\right)\:\Rightarrow \\ $$$$\mathrm{f}^{'} \left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi}…