Category: Integration

Question Number 94084 by seedhamaieng@gmail.com last updated on 16/May/20 $$\int \sqrt{\cot x}dx$$ Commented by Kunal12588 last updated on 16/May/20 $$=\int \sqrt{tan(\pi /2-x)}dx$$$$=-\int \sqrt{tant}dt;witht=tan(\frac{\pi }{2}-x)$$$$\int\sqrt{{tan}\:{x}}\:{dx}\:{is}\:{very}\:{popular}\:{integral},\:{its}\:{already} \…

Question Number 159612 by cortano last updated on 19/Nov/21 Answered by Ar Brandon last updated on 19/Nov/21 $$I=\int \frac{\sqrt{2+\sqrt[3]{x}}}{\sqrt[3]{x}}dx,x=u^3\Rightarrow dx=3u^{2}du$$$$=3\int \frac{\sqrt{2+u}}{u}\cdot u^{2}du=3\int u\sqrt{2+u}du$$$$\:\:\:=\mathrm{3}\int\left({u}+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…

Question Number 28541 by abdo imad last updated on 26/Jan/18 $$provethat{\int }_0^{\mathrm{\infty }}\frac{sinx}{e^{ax}-1}dx=\sum _{p=1}^{\mathrm{\infty }}\frac{1}{1+p^2{a}^2}witha>0$$ Terms of Service Privacy Policy…

Question Number 159597 by mathlove last updated on 19/Nov/21 Answered by mr W last updated on 19/Nov/21 $${\left(\frac{{\sin }^{2014}x\sin \left(2014x\right)}{2014}\right)}^{\prime }$$$$=\frac{2014{\sin }^{2013}x\cos x\sin \left(2014x\right)+\sin {}^{2014}x\times 2014\cos \left(2014x\right)}{2014}$$$$=\mathrm{sin}^{\mathrm{2013}}…

Question Number 159552 by Ar Brandon last updated on 18/Nov/21 Commented by Ar Brandon last updated on 18/Nov/21 $$\mathrm{Prove}\mathrm{the}\mathrm{above}\mathrm{results}$$ Commented by mindispower last…