Primitive of Tangent of a x
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Theorem
Secant Form
- $\ds \int \tan a x \rd x = \frac {\ln \size {\sec a x} } a + C$
Cosine Form
- $\ds \int \tan a x \rd x = \frac {-\ln \size {\cos a x} } a + C$
Examples
Tangent of $2 x$
- $\ds \int \tan 3 x \rd x = \frac 1 2 \ln \size {\sec 2 x} + C$