Question Number 212050 by Spillover last updated on 28/Sep/24
Answered by Ghisom last updated on 28/Sep/24
![∫(x/( (√((x^2 +1)(1+(√(x^2 +1)))))))dx= [t=2(√(1+(√(x^2 +1))))] =∫dt=t= =2(√(1+(√(x^2 +1))))+C](https://www.tinkutara.com/question/Q212064.png)
$$\int\frac{{x}}{\:\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}\sqrt{\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\right] \\ $$$$=\int{dt}={t}= \\ $$$$=\mathrm{2}\sqrt{\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}+{C} \\ $$
Commented by Spillover last updated on 28/Sep/24
$${great}.{thanks} \\ $$
Answered by Spillover last updated on 28/Sep/24
