Find $ \displaystyle \displaystyle\int \frac{3}{(x+1)(x-1)} \, \mathrm{d}x$; \( \displaystyle \dis

Question

Find $ \displaystyle \displaystyle\int \frac{3}{(x+1)(x-1)} \, \mathrm{d}x$; $ \displaystyle \displaystyle\int \frac{x+3}{x(x+1)} \, \mathrm{d}x $.

Accepted Answer

(a) $\frac32\ln\left|\frac{x-1}{x+1}\right|+C$, $x\ne\pm1$. (b) $3\ln|x|-2\ln|x+1|+C$, $x\ne0,-1$.

Indefinite integrals of rational functions using partial fraction decomposition