Primitive of Tangent of a x

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 $2 x$

$\ds \int \tan 3 x \rd x = \frac 1 2 \ln \size {\sec 2 x} + C$

Also see

• Primitive of $\sin a x$
• Primitive of $\cos a x$
• Primitive of $\cot a x$
• Primitive of $\sec a x$
• Primitive of $\csc a x$