Question Number 201548 by Calculusboy last updated on 08/Dec/23
Answered by MathematicalUser2357 last updated on 20/Jan/24
![[−(x−1){2(√(1−x^2 ))+(√(1−x))x−2x+(√(1−x))−2(√(x+1))log((√(1−x))+1)−(√(x+1))log x+2(√(x+1))log((√(x+1))+1)−2}−(√(1−x))(√(1−x^2 ))tanh^(−1) (√(1−x^2 ))]+C](https://www.tinkutara.com/question/Q202846.png)
$$\left[−\left({x}−\mathrm{1}\right)\left\{\mathrm{2}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{x}}{x}−\mathrm{2}{x}+\sqrt{\mathrm{1}−{x}}−\mathrm{2}\sqrt{{x}+\mathrm{1}}\mathrm{log}\left(\sqrt{\mathrm{1}−{x}}+\mathrm{1}\right)−\sqrt{{x}+\mathrm{1}}\mathrm{log}\:{x}+\mathrm{2}\sqrt{{x}+\mathrm{1}}\mathrm{log}\left(\sqrt{{x}+\mathrm{1}}+\mathrm{1}\right)−\mathrm{2}\right\}−\sqrt{\mathrm{1}−{x}}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\mathrm{tanh}^{−\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right]+{C} \\ $$