How would you integrate tan5xdx ?

Question

Thanks in advance.

Can you use u substitution?

Answer 1

try taking the derivative of
ln(cosx)

that should give you a good hint

Answer 2

I know you get -sin x; I know how to do the problem without the 5, but I don't understand how to do the problem since it is tangent of 5x

Answer 3

The derivative of ln(cosx) is actually
-tanx, not -sinx. "ln" means "natural (base e) logarithm of..

For the integral of tan 5x, let u = 5x
tan 5x = u
du = 5 dx

integral of tan(5x) dx
= integral of (1/5) tan u du
= -(1/5)ln cos u
= -(1/5)ln cos(5x)