Category: Integration

Question Number 167024 by peter frank last updated on 04/Mar/22 $$\int \sec \theta \tan {}^4\theta \mathrm{d}\theta$$ Answered by cortano1 last updated on 05/Mar/22 $$\mathrm{let}\mathrm{t}=\tan \theta$$$$\mathrm{I}=\int\:\frac{\mathrm{t}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}}…

Question Number 35949 by ajfour last updated on 26/May/18 $${\int }_0^{\alpha }\frac{\tan \theta }{\sqrt{a^2\cos {}^2\theta -b^2\sin {}^2\theta }}d\theta =?$$ Commented by abdo mathsup 649 cc last…

Question Number 101461 by Dwaipayan Shikari last updated on 02/Jul/20 Answered by MAB last updated on 02/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\:\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} }=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\frac{{r}}{{n}}}\left(\mathrm{3}\sqrt{\frac{{r}}{{n}}}+\mathrm{4}\right)^{\mathrm{2}}…

Question Number 101451 by yahyajan last updated on 02/Jul/20 Commented by Dwaipayan Shikari last updated on 02/Jul/20 $${sin}^{-1}x\int 1dx-\int \frac{x}{\sqrt{1-x^2}}dx$$$${xsin}^{−\mathrm{1}} {x}\:+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}\:\:\:={xsin}^{−\mathrm{1}} {x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…

Question Number 166956 by mnjuly1970 last updated on 03/Mar/22 $$$$$$calculate$$$${\int }_0^{\mathrm{\infty }}\frac{\sqrt{x}arctan\left(x\right)}{1+x^2}dx=?$$ Answered by ArielVyny last updated on…