Calculus Examples

$\int x \sec^{2} (x) d x$

Step 1

Integrate by parts using the formula $\int u d v = u v - \int v d u$ , where $u = x$ and $d v = \sec^{2} (x)$ .

$x \tan (x) - \int \tan (x) d x$

Step 2

The integral of $\tan (x)$ with respect to $x$ is $\ln (| \sec (x) |)$ .

$x \tan (x) - (\ln (| \sec (x) |) + C)$

Step 3

Simplify.

$x \tan (x) - \ln (| \sec (x) |) + C$