Category: Integration

Question Number 86615 by ar247 last updated on 29/Mar/20 $$\int \sqrt{tanx}dx$$ Commented by Ar Brandon last updated on 29/Mar/20 $$let{t}^2=tanx\Rightarrow 2tdt={sec}^{2}xdx$$$$\Rightarrow{dx}=\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{4}}…

Question Number 21076 by j.masanja06@gmail.com last updated on 11/Sep/17 $$integratewithrespecttox$$$$\int x^{sinx}$$ Answered by FilupS last updated on 17/Sep/17 $$\int{x}^{\mathrm{sin}\left({x}\right)} {dx}=\int{e}^{\mathrm{sin}\left({x}\right)\mathrm{ln}\left({x}\right)} {dx} \…

Question Number 86611 by Ar Brandon last updated on 30/Mar/20 $${\int }_1^e\frac{\ln \mathrm{x}}{\mathrm{x}+1}\mathrm{dx}$$ Answered by Ar Brandon last updated on 30/Mar/20 Terms of…

Question Number 152147 by john_santu last updated on 26/Aug/21 Answered by Ar Brandon last updated on 26/Aug/21 $$I_n={\int }_{-1}^1(\sqrt{x^2+\frac{1}{n}}-\mid x\mid )dx$$$$\:\:\:\:=\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 152142 by Ar Brandon last updated on 26/Aug/21 $${\int }_0^1\frac{x}{{(1-x+x^2)}^2}\ln \left(\ln \frac{1}{x}\right)dx=-\frac{\gamma }{3}-\frac{1}{3}\ln \frac{6\sqrt{3}}{\pi }+\frac{\pi \sqrt{3}}{27}(5\ln 2\pi -6\ln \mathrm{\Gamma }\left(\frac{1}{6}\right))$$ Answered by mindispower last updated on 28/Aug/21 $$\int_{\mathrm{0}}…