Category: Integration

Question Number 85801 by mathmax by abdo last updated on 24/Mar/20 $$calculate{\int }_0^{\pi }\frac{dx}{{(cosx+2sinx)}^2}$$ Commented by john santu last updated on 25/Mar/20…

Question Number 20257 by tammi last updated on 24/Aug/17 $$\int \frac{dx}{(1-x)\sqrt{1+x}}$$ Answered by Tinkutara last updated on 24/Aug/17 $$t^2=x+1$$$$dx=2tdt$$$$\int\frac{\mathrm{2}{tdt}}{\left(\mathrm{2}\:−\:{t}^{\mathrm{2}}…

Question Number 20256 by tammi last updated on 24/Aug/17 $$\int \frac{dx}{(x-4)\sqrt{x+3}}$$ Answered by Tinkutara last updated on 24/Aug/17 $$x+3=t^2$$$$dx=2tdt$$$${x}\:−\:\mathrm{4}\:=\:{t}^{\mathrm{2}} \:−\:\mathrm{7}…

Question Number 20254 by tammi last updated on 24/Aug/17 $$\int \frac{dx}{(x-1)\sqrt{x^2+1}}$$ Answered by $@ty@mlastupdatedon25/Aug/17$$Letx-1=\frac{1}{t}$$$$\Rightarrow{dx}=\frac{−\mathrm{1}}{{t}^{\mathrm{2}} }{dt} \…

Question Number 85781 by Joel578 last updated on 24/Mar/20 $${\int }_0^1{\left(\ln \frac{1}{x}\right)}^{-3/2}dx$$ Commented by Joel578 last updated on 24/Mar/20 $$\mathrm{If}\mathrm{we}\mathrm{use}u=\ln \frac{1}{x},\mathrm{the}\mathrm{integral}\mathrm{will}\mathrm{become}$$$$\int_{\mathrm{0}}…