Category: Integration

Question Number 55560 by Tawa1 last updated on 26/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Feb/19 $$x=tana$$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sec}^{\mathrm{6}} {a}×{sec}^{\mathrm{2}} {ada}}{\left({tan}^{\mathrm{4}} {a}+{sec}^{\mathrm{2}} {a}\right)^{\frac{\mathrm{5}}{\mathrm{2}}}…

Question Number 121029 by bramlexs22 last updated on 05/Nov/20 Commented by bobhans last updated on 05/Nov/20 $$supermacho\dots !$$ Answered by MJS_new last updated on…

Question Number 186531 by normans last updated on 05/Feb/23 $$$$$$\mathbb{Q}.\mathit{u}\mathit{s}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{a}\mathit{r}\mathit{s}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{r}\mathit{e}\mathit{l}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{o}\mathit{f}\mathit{h}\mathit{a}\mathit{n}\mathit{k}\mathit{e}\mathit{l}\mathit{t}\mathit{r}\mathit{a}\mathit{n}\mathit{s}\mathit{f}\mathit{r}\mathit{o}\mathit{m}\mathit{t}\mathit{o}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{a}\mathit{t}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{I}\mathit{n}\mathit{t}\mathit{e}\mathit{g}\mathit{r}\mathit{a}\mathit{l}$$$${\stackrel{\mathrm{\infty }}{\int }}_0\frac{{\mathit{J}}_{\mathit{\gamma }+1}\left(\mathit{a}\mathit{r}\right){\mathit{J}}_{\mathit{\gamma }+1}\left(\mathit{b}\mathit{r}\right)}{\mathit{r}},\mathit{f}\mathit{o}\mathit{r}\mathit{\gamma }>-\frac{1}{2},0<\mathit{a}<\mathit{b}$$$$\mathit{w}\mathit{h}\mathit{e}\mathit{r}\mathit{e}{\mathit{J}}_{\mathit{n}}\left(\mathit{x}\right)\mathit{a}\mathit{r}\mathit{e}\mathit{b}\mathit{e}\mathit{s}\mathit{s}\mathit{e}\mathit{l}\mathit{f}\mathit{u}\mathit{n}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{s}.$$$$$$…

Question Number 55454 by maxmathsup by imad last updated on 24/Feb/19 $$letf\left(a\right)={\int }_0^{\mathrm{\infty }}\frac{ln\left(x\right)}{x^2+a}witha>0$$$$1)calculatef\left(a\right)intermsofa$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{2}}{dx}…

Question Number 120970 by Algoritm last updated on 04/Nov/20 Answered by mathmax by abdo last updated on 04/Nov/20 $$\mathrm{I}={\int }_0^{\pi }\frac{\ln (1+\frac{\mathrm{cosx}}{2})}{\mathrm{cosx}}\mathrm{dx}\mathrm{let}\mathrm{f}\left(\mathrm{a}\right)={\int }_0^{\pi }\frac{\ln (1+\mathrm{acosx})}{\mathrm{cosx}}\mathrm{dx}\mathrm{with}\mid \mathrm{a}\mid <1$$$$\mathrm{I}\:=\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\:\mathrm{we}\:\mathrm{hsve}\:\mathrm{f}^{'}…