Category: Integration

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 $$\int_{\mathbb{R}} \frac{\mathrm{e}^{\mathrm{its}} }{\mathrm{s}+\mathrm{3}}\mathrm{ds} \\ $$ 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 $$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{x2}^{\mathrm{x}} +\mathrm{7}}{\mathrm{3}^{\mathrm{x}} +\mathrm{lnx}+\mathrm{1}}\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 11/Jun/21…

Question Number 12101 by Nayon last updated on 13/Apr/17 $${Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{tan}^{−\mathrm{1}} \left({x}\right)}{\:{x}}{dx} \\ $$ 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}\begin{pmatrix}{{x}=\mathrm{1}\Rightarrow\varphi=\frac{\pi}{\mathrm{4}}}\\{{x}=\mathrm{0}\Rightarrow\varphi=\mathrm{0}}\end{pmatrix} \\…

Question Number 12098 by Nayon last updated on 13/Apr/17 $${Evaluate}\:\int\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$$$ \\ $$ Answered by sma3l2996 last updated on 13/Apr/17…