Integrating a single function and reduction of powers \(\displaystyle \displaystyle\int \ln x \, \ma

Question

Integrating a single function and reduction of powers $\displaystyle \displaystyle\int \ln x \, \mathrm{d}x$ $\displaystyle \displaystyle\int \arcsin x \, \mathrm{d}x$ $\displaystyle \displaystyle\int x^2 \sin x \, \mathrm{d}x$

Accepted Answer

(a) $x\ln x-x+C$, $x>0$. (b) $x\sin^{-1}x+\sqrt{1-x^2}+C$, $-1<x<1$. (c) $-x^2\cos x+2x\sin x+2\cos x+C$.

Integration by parts using LIATE rule

Integration by parts using LIATE rule

Solution:

Solution locked