Category: Integration

Question Number 73179 by mathmax by abdo last updated on 07/Nov/19 $$caoculate{\int }_0^{\mathrm{\infty }}\frac{arctan(x^2-1)}{2x^2+1}dx$$ Commented by mathmax by abdo last updated…

Question Number 73181 by mathmax by abdo last updated on 07/Nov/19 $$calculate{\int }_1^3\frac{x-2}{\sqrt{x^2+x+1}}dx$$ Commented by mathmax by abdo last updated on…

Question Number 138710 by bramlexs22 last updated on 17/Apr/21 $${\underset{1}{\int }}^{\mathrm{\infty }}\frac{\ln x}{(1+x)(1+x^2)}dx=?$$ Answered by mathmax by abdo last updated on 17/Apr/21 $$\Phi=\int_{\mathrm{1}}…

Question Number 138691 by liberty last updated on 16/Apr/21 $$\int \cos 2x\sqrt{1+\sin {}^{2}x}dx=?$$ Answered by mathmax by abdo last updated on 17/Apr/21 $$\mathrm{I}=\int\:\mathrm{cos}\left(\mathrm{2x}\right)\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:\Rightarrow\mathrm{I}=\int\:\mathrm{cos}\left(\mathrm{2x}\right)\sqrt{\mathrm{1}+\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{2}}}\mathrm{dx} \…

Question Number 138683 by mnjuly1970 last updated on 16/Apr/21 $$\dots nice..\dots \dots calculus\dots$$$$findthevalueof:$$$$\mathrm{\Theta }=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^n{sin}^2\left(n\right)}{n}=?$$$$\dots \dots \dots \dots \dots \dots \dots \dots .$$ Answered by Dwaipayan…