Category: Integration

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}}…

Question Number 83960 by john santu last updated on 08/Mar/20 $$\int \frac{\mathrm{x}-1}{\sqrt{{\mathrm{x}}^2-\mathrm{x}}}\mathrm{dx}?$$ Commented by mathmax by abdo last updated on 08/Mar/20 $${I}\:=\int\:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −{x}}}{dx}\:\Rightarrow\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{2}{x}−\mathrm{1}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}}…

Question Number 18396 by Joel577 last updated on 20/Jul/17 $$\int \sqrt{1+\frac{1}{x^2}+\frac{1}{{(x+1)}^2}}dx$$ Answered by b.e.h.i.8.3.417@gmail.com last updated on 20/Jul/17 $$\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\left({x}^{\mathrm{2}} +{x}\right)^{\mathrm{2}}…