Find the following integrals in Exercises: (ax^2+bx+c) dx - Vidyadip

Question

Find the following integrals in Exercises:
$\int(\text{ax}^2+\text{bx}+\text{c})\text { dx}$

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Answer

$\int(\text{ax}^2+\text{bx}+\text{c)}\text{ dx}$
$=\int\text{ax}^2 \text{ dx}+\int\text{bx}\text{ dx}+\int\text{c}\text{ dx}$
$=\text{a}\int\text{x}^2\text{ dx}+\text{b}\int\text{x}+\text{dx}+c\int1\text{ dx}$
$=\text{a}\frac{\text{x}^3}{3}+\text{b}\frac{\text{x}^2}{2}+\text{cx}+\text{c}_{1}$
where $\text{c}_{1}$ is the constant of integration.

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