Question
Integrate the function in Exercise:
$\frac{\text{x}\cos^{-1}\text{x}}{\sqrt{1-\text{x}^2}}$
$\frac{\text{x}\cos^{-1}\text{x}}{\sqrt{1-\text{x}^2}}$
$=\frac{-1}{2}\Bigg[\cos^{-1}\text{x}.2\sqrt{1-\text{x}^2}-\int\frac{-1}{\sqrt{1-\text{x}^2}}.2\sqrt{1-\text{x}^2}\text{dx}\Bigg]\frac{-1}{2}\Bigg[\cos^{-1}\text{x}.2\sqrt{1-\text{x}^2}-\int\frac{-1}{\sqrt{1-\text{x}^2}}.2\sqrt{1-\text{x}^2}\text{dx}\Bigg]$
$=\frac{-1}{2}\Big[2\sqrt{1-\text{x}^2}\cos^{-1}\text{x}-\int2\text{dx}\Big]$ $=\frac{-1}{2}\Big[2\sqrt{1-\text{x}^2}\cos^{-1}\text{x}+2\text{x}\Big]+\text{C}$ $=-\Big[\sqrt{1-\text{x}^2}\cos^{-1}\text{x}+\text{x}\Big]+\text{C}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.