Category: Integration

Question Number 8281 by tawakalitu last updated on 06/Oct/16 $$\int \frac{6\mathrm{sinx}\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}$$ Answered by Yozzias last updated on 06/Oct/16 $$\frac{\mathrm{sinx}}{\mathrm{sinx}+\mathrm{cosx}}=1-\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}$$$$\therefore \mathrm{I}=\int \frac{\mathrm{sinxcosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\int (1-\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}})\mathrm{cosxdx}$$$$=\int\left(\mathrm{cosx}−\frac{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}{\mathrm{sinx}+\mathrm{cosx}}\right)\mathrm{dx}…

Question Number 73751 by ~blr237~ last updated on 15/Nov/19 $$Findoutthevalueof$$$$J={\int }_0^{\mathrm{\infty }}{\int }_0^1(2e^{-2xy}-e^{-xy})dxdy$$ Commented by mathmax by abdo…

Question Number 139282 by qaz last updated on 25/Apr/21 $${\int }_0^{\mathrm{\infty }}\frac{lnx}{x^2+a^2}dx=\frac{\pi }{2a}\cdot lna,a>0$$ Answered by Ar Brandon last updated on 25/Apr/21 $$\Omega=\int_{\mathrm{0}}…

Question Number 139259 by bobhans last updated on 25/Apr/21 $$\int \frac{\cos \mathrm{x}+\sqrt[3]{7}}{\sin \mathrm{x}+\sqrt{6}}\mathrm{dx}=?$$ Answered by Dwaipayan Shikari last updated on 25/Apr/21 $$\int \frac{cosx+\sqrt[3]{7}}{sinx+\sqrt{6}}dx=log(sinx+\sqrt{6})+\sqrt[3]{7}\int \frac{1}{sinx+\sqrt{6}}dx$$$$={log}\left({sinx}+\sqrt{\mathrm{6}}\right)+\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{7}}\:\int\frac{\mathrm{1}}{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\sqrt{\mathrm{6}}}.\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:{tan}\frac{{x}}{\mathrm{2}}={t}…

Question Number 139248 by ajfour last updated on 24/Apr/21 $${\int }_a^{b}f\left(t\right)g^{\prime }\left(t\right)dt=?$$ Answered by mathmax by abdo last updated on 25/Apr/21 $$\int_{\mathrm{a}} ^{\mathrm{b}}…