Antiderivatives of Trigonometric Functions

In this section more formulas for antiderivatives are to be justified.

Antiderivative of the Tangent Function

In order to calculate the antiderivative of the tangent function, multiply by 1 written as $\nicefrac{\sec u}{\sec u}$ , and then apply the formula $\int \nicefrac{dv}{v} = \ln |v| + C$ .

$\begin{eqnarray*} \int \!\tan u\cdot du &=& \int\frac{\sec u\cdot \tan u}{\sec u}\cdot du \\ &=& \ln |\sec u| + C \end{eqnarray*}$

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Antiderivatives of Trigonometric Functions

The antiderivative of trigonometric functions are deduced.

Antiderivative of the Tangent Function