Category: Integration

Question Number 149625 by puissant last updated on 06/Aug/21 $$1){\int }_0^{2\pi }\frac{1}{\mathrm{a}+\sin \left(\mathrm{t}\right)}\mathrm{dt},\mathrm{a}>0$$$$2){\int }_{2\pi }^{4\pi }\frac{1}{2+\sin \left(\mathrm{t}\right)}\mathrm{dt}..$$ Answered by ArielVyny last updated on 06/Aug/21…

Question Number 149608 by puissant last updated on 06/Aug/21 $$\dots ..\mathrm{K}=\int \frac{1}{1+{\sin }^2\left(\mathrm{x}\right)}\mathrm{dx}\dots \dots$$ Answered by ArielVyny last updated on 06/Aug/21 $${sin}^{2}x=\frac{1-cos\left(2x\right)}{2}$$$${K}=\int\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}}=\int\frac{\mathrm{1}}{\frac{\mathrm{2}+\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}}{dx} \…

Question Number 84036 by M±th+et£s last updated on 08/Mar/20 $${\int }_{-1}^{10}sin(x-\mid x\mid )dx$$ Answered by TANMAY PANACEA last updated on 09/Mar/20 $$\int_{−\mathrm{1}} ^{\mathrm{0}} {sin}\left({x}+{x}\right){dx}+\int_{\mathrm{0}}…

Question Number 84035 by M±th+et£s last updated on 08/Mar/20 $$\int \frac{x-4}{x^4-1}dx$$ Commented by MJS last updated on 08/Mar/20 $$\frac{{x}−\mathrm{4}}{{x}^{\mathrm{4}} −\mathrm{1}}=−\frac{{x}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{5}}{\mathrm{4}\left({x}+\mathrm{1}\right)}−\frac{\mathrm{3}}{\mathrm{4}\left({x}−\mathrm{1}\right)} \…

Question Number 83984 by M±th+et£s last updated on 08/Mar/20 $$\int {cos}^7\left(x\right)dx$$ Answered by TANMAY PANACEA last updated on 08/Mar/20 $$\int {cos}^{6}x\times cosxdx$$$$\int\left(\mathrm{1}−{sin}^{\mathrm{2}}…