Prove

Question:

$\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$

Solution:

$\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$

$=\int\left(x+5-4 x^{-2}\right) d x$

$=\int x d x+5 \int 1 \cdot d x-4 \int x^{-2} d x$

$=\frac{x^{2}}{2}+5 x-4\left(\frac{x^{-1}}{-1}\right)+\mathrm{C}$

$=\frac{x^{2}}{2}+5 x+\frac{4}{x}+\mathrm{C}$

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