# Evaluate the following integral. \int 2x(1-x^{-3})dx

Evaluate the following integral.
$\int 2x\left(1-{x}^{-3}\right)dx$
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Alannej
$\int 2x\left(1-{x}^{-3}\right)dx=\int \left(2x-2{x}^{-2}\right)dx$
$=\left(2\frac{{x}^{2}}{2}-2\frac{{x}^{-2+1}}{-2+1}\right)+c$
Hence, $\int 2x\left(1-{x}^{-3}\right)dx={x}^{2}+\frac{2}{x}+c$