Category: Integration

Question Number 148026 by mnjuly1970 last updated on 25/Jul/21 $$$$$$\mathrm{A}:={\int }_{-1}^0{e}^{x+\frac{1}{x}}\mathrm{\&}a\mathrm{A}+e^b={\int }_0^{\mathrm{\infty }}{\left(\frac{1}{e}\right)}^{x+\frac{1}{x}}$$$$than:a+b=?a,b\in \mathbb{Z}$$$$$$ Answered…

Question Number 148000 by vvvv last updated on 25/Jul/21 $$\underset{-\mathrm{\infty }}{\stackrel{+\mathrm{\infty }}{\int }}\frac{\mathit{d}\mathit{x}}{{({\mathit{x}}^2+{\mathit{k}}^2)}^{\frac{3}{2}}}$$ Answered by gsk2684 last updated on 25/Jul/21 $$\mathrm{2}\underset{{x}=\mathrm{0}}…

Question Number 82446 by M±th+et£s last updated on 21/Feb/20 $$showthat$$$${\int }_0^{\mathrm{\infty }}{x}^{-log\left(x\right)}xlog\left(x\right)dx=e\sqrt{\pi }$$ Commented by abdomathmax last updated on 21/Feb/20 $${changement}\:{logx}={t}\:{give}\:{x}={e}^{{t}}…

Question Number 82440 by mathmax by abdo last updated on 21/Feb/20 $$find\int \frac{x+1}{x+2}\sqrt{\frac{1-x}{1+x}}dx$$ Commented by abdomathmax last updated on 24/Feb/20 $$letA=\int \frac{x+1}{x+2}\sqrt{\frac{1-x}{1+x}}dxchangement\sqrt{\frac{1-x}{1+x}}=t$$$${hive}\:\:\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}={t}^{\mathrm{2}} \:\Rightarrow\mathrm{1}−{x}={t}^{\mathrm{2}}…

Question Number 82435 by mathmax by abdo last updated on 21/Feb/20 $$calculate{\int }_4^{+\mathrm{\infty }}\frac{x^3}{{(2x+1)}^3{(x-3)}^5}dx$$ Commented by abdomathmax last updated on…