Posted by **Andrea** on Wednesday, March 4, 2009 at 6:33pm.

How would you integrate tan5xdx ?

Thanks in advance.

Can you use u substitution?

- calculus -
**Reiny**, Wednesday, March 4, 2009 at 6:39pm
try taking the derivative of

ln(cosx)

that should give you a good hint

- calculus -
**Andrea**, Wednesday, March 4, 2009 at 7:33pm
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

- calculus -
**drwls**, Wednesday, March 4, 2009 at 10:06pm
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)

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