Integral of $$$\tan{\left(u \right)} \sec{\left(u \right)}$$$

The calculator will find the integral/antiderivative of $$$\tan{\left(u \right)} \sec{\left(u \right)}$$$, with steps shown.

Related calculator: Definite and Improper Integral Calculator

Please write without any differentials such as $$$dx$$$, $$$dy$$$ etc.
Leave empty for autodetection.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Your Input

Find $$$\int \tan{\left(u \right)} \sec{\left(u \right)}\, du$$$.

Solution

The integral of $$$\tan{\left(u \right)} \sec{\left(u \right)}$$$ is $$$\int{\tan{\left(u \right)} \sec{\left(u \right)} d u} = \sec{\left(u \right)}$$$:

$${\color{red}{\int{\tan{\left(u \right)} \sec{\left(u \right)} d u}}} = {\color{red}{\sec{\left(u \right)}}}$$

Therefore,

$$\int{\tan{\left(u \right)} \sec{\left(u \right)} d u} = \sec{\left(u \right)}$$

Add the constant of integration:

$$\int{\tan{\left(u \right)} \sec{\left(u \right)} d u} = \sec{\left(u \right)}+C$$

Answer

$$$\int \tan{\left(u \right)} \sec{\left(u \right)}\, du = \sec{\left(u \right)} + C$$$A