Question

$\underset{0}{\overset{1}{\int }}\frac{x}{(x-2{)}^4}$ is equal to

• A. $-\frac{2}{3}$
• B. $-\frac{3}{4}$
• C. $-\frac{1}{8}$
• D. $-\frac{3}{8}$

Answer 1

The correct option is D $-\frac{3}{8}$

$\underset{1}{\overset{4}{\int }}\frac{x}{(x-2{)}^4}$
Let $x-2=t\Rightarrow x=t+2\Rightarrow dx=dt$
$\underset{-1}{\overset{2}{\int }}\frac{t+2}{t^4}dx=\underset{-1}{\overset{2}{\int }}\frac{1}{t^3}+\frac{2}{t^4}dx=[-\frac{1}{2t^2}-\frac{2}{3t^3}{]}_{-1}^2$
$[-\frac{1}{8}-\frac{1}{12}+\frac{1}{2}-\frac{2}{3}]=-\frac{3}{8}$