Find the following integrals in Exercises. x^3 + 5x^2-4 x~^2 dx - Vidyadip

Question

Find the following integrals in Exercises. $\int\frac{\text{x}^3 + 5\text{x}^2-4}{\text{x}~^2}\text{ dx}$

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Answer

$\int\frac{\text{x}^3+5\text{x}^2-4}{\text{x}^2}\text{ dx}$
$=\int\bigg(\frac{\text{x}^3}{\text{x}^2}+\frac{\text{5x}^2}{\text{x}^2}-\frac{\text{4}}{\text{x}^2}\bigg)\text{ dx}$
$=\int(\text{x}+\text{5}-4\text{x}^{-2})\text{ dx}$
$=\int\text{x}\text{ dx}+\int5\text{ dx}-\int4\text{x}^{-2}\text { dx} $
$=\int\text{x}\text{ dx}+5\int1\text{ dx}-4\int\text{x}^{-2}\text{ dx} $
$=\frac{\text{x}^2}{2}+5\text{x}+\frac{4}{\text{x}}+\text{c}$

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