Find the following integrals in Exercises: (2x-3 +e^x) dx - Vidyadip

Question

Find the following integrals in Exercises: $\int(2\text{x}-3\cos\text{x}+\text{e}^\text{x})\text{ dx}$

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Answer

$\int(2\text{x}-3\cos\text{x}+\text{e}^\text{x})\text{ dx}$
$=\int2\text{x}\text{ dx}-\int3 \cos\text{x dx}+\int\text{e}^\text{x}\text{ dx}$
$=2\int\text{x}\text{ dx}-3\int\cos\text {x}\text{ dx}+\int\text{e}^{\text{ x}}\text{ dx} $
$=2\frac{\text{x}^2}{2}-3\sin\text{x}+\text{e}^{\text{x}}+\text{c} $
$=\text{x}^2-3\sin\text{x }+\text{e}^{\text{x}}+\text{c} $

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