Question

$\int (x^{-3}+\cos 2x)dx$ equals

• A. $\frac{-x^{-2}}{2}+\frac{\sin 2x}{2}+c$
• B. $\frac{x^{-2}}{2}+\sin 2x+c$
• C. $\frac{-x^{-4}}{4}+\frac{\sin 2x}{2}+c$
• D. $\frac{-x^{-2}}{2}+\frac{\sin x}{2}+c$

Answer 1

The correct option is A $\frac{-x^{-2}}{2}+\frac{\sin 2x}{2}+c$

$\int (x^{-3}+\cos 2x)dx$ =
$\int \left(x^{-3}\right)dx+$$\int \left(\cos 2x\right)dx=$
$=\frac{x^{-3+1}}{-3+1}+\frac{\sin 2x}{2}+c$