Question Number 77103 by Boyka last updated on 03/Jan/20 Commented by turbo msup by abdo last updated on 03/Jan/20 $${let}\:{I}=\int\:\:\frac{\mathrm{2}}{\mathrm{2}+{sinx}}{dx}\:{changement} \\ $$$${tan}\left(\frac{{x}}{\mathrm{2}}\right)\:={t}\:{give}\: \\ $$$${I}=\int\:\:\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}×\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 142629 by qaz last updated on 03/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \centerdot\frac{\mathrm{2n}−\mathrm{1}}{\left(\mathrm{2n}\right)!}\centerdot\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2n}} \\ $$$$=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2n}−\mathrm{1}}{\left(\mathrm{2n}\right)!}\centerdot\left(−\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2}} \right)^{\mathrm{n}} \\ $$$$=\left(\mathrm{2xD}−\mathrm{1}\right)\mid_{\mathrm{x}=\pi/\mathrm{2}} \underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }{\left(\mathrm{2n}\right)!}…
Question Number 77086 by Dah Solu Tion last updated on 03/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {xtan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$ Commented by Tony Lin last updated…
Question Number 77089 by Dah Solu Tion last updated on 03/Jan/20 $$\boldsymbol{{Cheap}}\:\downdownarrows \\ $$$$\int\sqrt{\frac{\boldsymbol{{x}}}{\:\sqrt{\frac{\boldsymbol{{x}}}{\:\sqrt{\frac{\boldsymbol{{x}}}{…}}}}}}\boldsymbol{{dx}} \\ $$$$ \\ $$$$ \\ $$ Commented by Tony Lin last…
Question Number 77087 by Dah Solu Tion last updated on 03/Jan/20 $$\int_{\mathrm{0}} ^{\frac{\boldsymbol{{a}}}{\mathrm{2}}} \boldsymbol{{x}}^{\mathrm{2}} \left(\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{x}}^{\mathrm{2}} \right)^{\frac{−\mathrm{3}}{\mathrm{2}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{Help}}!!! \\ $$$$ \\ $$ Commented…
Question Number 11544 by Nayon last updated on 28/Mar/17 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:{Evaluate}\:\int{x}^{\mathrm{3}} {e}^{\mathrm{2}{x}} {dx} \\ $$$$ \\…
Question Number 142595 by qaz last updated on 02/Jun/21 $$\mathrm{Prove}\:::\:\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}=\mathrm{4}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\mathrm{1}}{\left[\left(\mathrm{2n}+\mathrm{1}\right)\pi−\mathrm{2x}\right]^{\mathrm{2}} }+\frac{\mathrm{1}}{\left[\left(\mathrm{2n}+\mathrm{1}\right)\pi+\mathrm{2x}\right]^{\mathrm{2}} }\right\} \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jun/21…
Question Number 142573 by mnjuly1970 last updated on 02/Jun/21 Answered by qaz last updated on 02/Jun/21 $$\mathrm{csc}\:\mathrm{x} \\ $$ Commented by mnjuly1970 last updated on…
Question Number 77036 by Master last updated on 02/Jan/20 Commented by mr W last updated on 02/Jan/20 $${if}\:{f}\left(−{x}\right)=−{f}\left({x}\right), \\ $$$$\int_{−{a}} ^{+{a}} {f}\left({x}\right)=\mathrm{0} \\ $$$$\Rightarrow\int_{−\mathrm{1}} ^{+\mathrm{1}}…
Question Number 142545 by mnjuly1970 last updated on 02/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:…..{integral} \\ $$$$\:\:\:\:\:\Omega:=\int_{−\infty} ^{\:\:+\infty} \frac{{dx}}{\left({x}^{\mathrm{2}} +\pi^{\mathrm{2}} \right){cosh}\left({x}\right)}\:=? \\ $$$$….. \\ $$ Answered by mindispower…