Category: Integration

Question Number 176594 by mnjuly1970 last updated on 22/Sep/22 $$$$$$\mathit{\varphi }={\int }_0^1\frac{{\left({tanh}^{-1}\left(x\right)\right)}^2}{{(1+x)}^2}dx=?$$$$\prec solution\succ$$$$note:{tanh}^{-1}\left(x\right)=-\frac{1}{2}ln\left(\frac{1-x}{1+x}\right)$$$$\:\:\:\:\:\boldsymbol{\phi}=\:\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\mathrm{1}}…

Question Number 111048 by mohammad17 last updated on 01/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 176570 by mathlove last updated on 21/Sep/22 $$\left(1\right){\underset{\frac{\pi }{3}}{\int }}^{\frac{\pi }{2}}\frac{1+sinx}{cosx}dx=?$$ Answered by Peace last updated on 21/Sep/22 $$\int \frac{1+sin\left(x\right)}{cos\left(x\right)}dx=\int \frac{cos\left(x\right)}{{cos}^2\left(x\right)}+\int \frac{sin\left(x\right)}{cos\left(x\right)}dx$$$$=\int\frac{{cos}\left({x}\right)}{\mathrm{1}−{sin}^{\mathrm{2}}…

Question Number 176566 by mnjuly1970 last updated on 21/Sep/22 $$----$$$$calculate:\mathrm{\Phi }=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{(2n+1).e^{4n+2}}=?$$$$where{}^{″}e{}^{″}iseulernumber.$$$$\prec solution\succ$$$$\:\:\:\:\:\:\Phi\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{e}^{\:\mathrm{4}{n}+\mathrm{2}} }\:\int_{\mathrm{0}} ^{\:\mathrm{1}}…

Question Number 111025 by mathmax by abdo last updated on 01/Sep/20 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\frac{{\mathrm{x}}^2\ln \left(\mathrm{x}\right)}{{(1+\mathrm{x})}^4}\mathrm{dx}$$ Answered by mathdave last updated on 01/Sep/20…