Primitive of Tangent of a x/Examples/2 x

Example of Use of Primitive of $\tan a x$

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

Proof

From Primitive of $\tan a x$: Secant Form:

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

The result follows by setting $a = 2$.

$\blacksquare$

Proof

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XIV}$: $2$.