Evaluate 3 x^3-2 x x d x - Vidyadip

Question

Evaluate $\int \frac{3 x^3-2 \sqrt{x}}{x} d x$

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Answer

$
\begin{aligned}
& \int \frac{3 x^3-2 \sqrt{x}}{x} d x \\
= & \int\left(\frac{3 x^3}{x}-\frac{2 \sqrt{x}}{x}\right) d x \\
= & \int\left(3 x^2-\frac{2}{\sqrt{x}}\right) d x \\
= & 3 \int x^2 d x-2 \int x^{-\frac{1}{2}} d x
\end{aligned}
$
$
\begin{aligned}
& =3 \cdot\left(\frac{x^3}{3}\right)-2 \cdot\left[\frac{x^{\frac{1}{2}}}{\left(\frac{1}{2}\right)}\right]+c \\
& =x^3-4 \sqrt{x}+c .
\end{aligned}
$

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