Question

The value of \( \int_{0}^{\infty} \frac{d x}{(1+x)^{3}} \) is:

Answer 1

\(\int_{0}^{\infty}\frac{\displaystyle{dx}}{\displaystyle{(1+x)^3}} = \left.\frac{\displaystyle{-1}}{\displaystyle{2(1+x)^2}}\right|_0^\infty =0.5 \\ Remember \:that\\ \int \frac{1}{x^n}dx =\int x^{-n}dx = \frac{\displaystyle{x^{-n+1}}}{\displaystyle{-n+1}} + C \)