Find the following integrals in Exercises: 2-3 ^2x dx - Vidyadip

Question

Find the following integrals in Exercises: $\int\frac{2-3\sin\text{x}}{\cos^2\text{x}}\text{ dx}$

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Answer

$\int\frac{2-3\sin\text{x}}{\cos^2\text{x}}\text{ dx}=\int\bigg(\frac{2}{\cos^2\text{x}}-\frac{3\sin\text{x}}{\cos^2\text{x}}\bigg)\text{ dx} $
$= \int(2\sec^2\text{x}-3\tan\text{x }\sec\text{x})\text{ dx} $
$=2\int\sec^2\text{x}\text{ dx}-3\int\sec\text{x}\tan\text{x}\text{ dx} $
$=2\tan\text{x}-3\sec\text{x}+\text{c} $

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