Category: Integration

Question Number 77675 by TawaTawa last updated on 08/Jan/20 $${\int }_0^{\mathrm{\infty }}3{(2\mathrm{x}-\frac{3}{\mathrm{x}})}^2\mathrm{dx}$$ Answered by mind is power last updated on 09/Jan/20 $$\mathrm{diverge}\:…

Question Number 12130 by sujith last updated on 14/Apr/17 $$\int \sqrt{a+x/a-x}$$$$-\sqrt{a-x/a+x}$$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17 $$\frac{{a}+{x}}{{a}−{x}}={t}^{\mathrm{2}} \Rightarrow\frac{{a}+{x}−{a}+{x}}{{a}+{x}+{a}−{x}}=\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{2}} +\mathrm{1}}\Rightarrow{x}={a}\frac{{t}^{\mathrm{2}}…

Question Number 143190 by Ar Brandon last updated on 11/Jun/21 $${\int }_{\mathbb{R}}\frac{{\mathrm{e}}^{\mathrm{its}}}{\mathrm{s}+3}\mathrm{ds}$$ Commented by mohammad17 last updated on 11/Jun/21 $${w}=\frac{\mathrm{1}}{{s}+\mathrm{3}}\Rightarrow{s}=\frac{\mathrm{1}}{{w}}−\mathrm{3}\Rightarrow{ds}=−\frac{\mathrm{1}}{{w}^{\mathrm{2}} }{dw} \…

Question Number 143178 by Ar Brandon last updated on 10/Jun/21 $${\int }_1^{\mathrm{\infty }}\frac{{\mathrm{x}2}^{\mathrm{x}}+7}{3^{\mathrm{x}}+\mathrm{lnx}+1}\mathrm{dx}$$ Commented by Dwaipayan Shikari last updated on 11/Jun/21…

Question Number 12101 by Nayon last updated on 13/Apr/17 $$Evaluate{\int }_0^1\frac{{tan}^{-1}\left(x\right)}{x}dx$$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/Apr/17 $${x}={tg}\varphi\Rightarrow{dx}=\frac{{d}\varphi}{\mathrm{1}+{tg}^{\mathrm{2}} \varphi}$$\left(\begin{array}{c}x=1\Rightarrow \phi =\frac{\pi }{4}\\ x=0\Rightarrow \phi =0\end{array}\right)$$ \…