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

Question

Find the following integrals in Exercises: $\int\frac{\sec^2\text{x}}{\text{cosec}^2\text{x}}\text{ dx}$

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Answer

$\int\frac{\sec^2\text{x}}{\text{cosec}^2\text{x}}\text{ dx}$ $=\int\frac{\frac{1}{\cos^2\text{x}}}{\frac{1}{\sin^2\text{x}}}\text{ dx} $
$=\int\frac{\sin^2\text{x}}{\cos^2\text{x}}\text{ dx}=\int\tan^2\text{x}\text{ dx} $
$=\int(\sec^2\text{x}-1)\text{ dx}$
$\int\sec^2\text{x}\text{ dx}-\int1\text{ dx}=\tan\text{x}- \text{x}+\text{c} $

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