Category: Integration

Question Number 189496 by Tawa11 last updated on 17/Mar/23 $$\int {\mathrm{xe}}^{\frac{{\mathrm{x}}^2}{2}}\mathrm{dx}$$ Answered by BaliramKumar last updated on 18/Mar/23 $$let\frac{x^2}{2}=y$$$$\frac{\mathrm{2}{x}}{\mathrm{2}}\:=\:\frac{{dy}}{{dx}}\:\Rightarrow\:{xdx}\:=\:{dy}…

Question Number 123937 by mnjuly1970 last updated on 29/Nov/20 $$\dots nicecalculus\dots$$$$provethat::$$$${\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}\frac{(\pi -4x)tan\left(x\right)}{1-tan\left(x\right)}dx\stackrel{???}{=}\pi ln\left(2\right)-\frac{{\pi }^2}{4}$$$$$$ Answered by Dwaipayan…

Question Number 123920 by john_santu last updated on 29/Nov/20 $$\int \frac{(x-1)\sqrt{x^4+2x^3-x^2+2x+1}}{x^2(x+1)}dx?$$ Answered by liberty last updated on 29/Nov/20 $$\left(\bullet\right)\:\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:=\:\frac{{x}^{\mathrm{2}}…

Question Number 123896 by john_santu last updated on 29/Nov/20 $$\underset{0}{\stackrel{\pi }{\int }}\frac{\sin {}^{2}x}{\sqrt{x}}dx$$ Answered by mindispower last updated on 29/Nov/20 $${sin}^{\mathrm{2}} \left({x}\right)=\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}} \…

Question Number 123866 by benjo_mathlover last updated on 28/Nov/20 $$Tomrmjssir.$$$$integrallover$$$$\underset{0}{\stackrel{\pi /4}{\int }}\frac{\tan (\frac{\pi }{4}-x)}{\cos {}^{2}x\sqrt{\tan {}^{3}x+\tan {}^{2}x+\tan x}}dx=?$$ Answered by liberty last…