Calculus Examples

$\int \frac{e^{\tan (x)}}{\cos^{2} (x)} d x$

Step 1

Convert from $\frac{1}{\cos^{2} (x)}$ to $\sec^{2} (x)$ .

$\frac{d}{d x} [\int e^{\tan (x)} \sec^{2} (x) d x]$

Step 2

$\int e^{\tan (x)} \sec^{2} (x) d x$ is an antiderivative of $e^{\tan (x)} \sec^{2} (x)$ , so by definition $\frac{d}{d x} [\int e^{\tan (x)} \sec^{2} (x) d x]$ is $e^{\tan (x)} \sec^{2} (x)$ .

$e^{\tan (x)} \sec^{2} (x)$