Category: Integration

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Question Number 192212 by josemate19 last updated on 11/May/23 $$\int -1^{x}dx$$ Answered by Frix last updated on 12/May/23 $$\int -1^{x}dx=-\int 1^{x}dx=-\int dx=-x+C$$$$\int\left(−\mathrm{1}\right)^{{x}}…

Question Number 126604 by bramlexs22 last updated on 22/Dec/20 $$\int \frac{dx}{(1-x^2)\sqrt[4]{2x^2-1}}?$$ Answered by liberty last updated on 22/Dec/20 $${Y}=\int\:\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:\sqrt[{\mathrm{4}}]{\mathrm{2}{x}^{\mathrm{2}}…

Question Number 61056 by Tawa1 last updated on 28/May/19 $$\int \frac{\mathrm{x}+\sin \left(\mathrm{x}\right)}{1+\cos \left(\mathrm{x}\right)}\mathrm{dx}$$ Answered by perlman last updated on 28/May/19 $$cos\left(x\right)=2{cos}^2\left(\frac{x}{2}\right)-1$$$$\frac{{x}+{sin}\left({x}\right)}{\mathrm{1}+{cos}\left({x}\right)}=\frac{{x}+{sin}\left({x}\right)}{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}=\frac{{x}}{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}+\frac{\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}\right){cos}\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{2}{cos}^{\mathrm{2}}…