# Math Help - Quick Question - Integration

1. ## Quick Question - Integration

While doing some exercises in my cal II book i stumbled on these 2 questions.. Any help will be appreciated. Thanks

(1) The integral of tan3x --> -1/3ln|cos3x|?
(2) The integral of x/(x^(2)-1)^2 --> not sure

2. Originally Posted by Bure03
While doing some exercises in my cal II book i stumbled on these 2 questions.. Any help will be appreciated. Thanks

(1) The integral of tan3x --> -1/3ln|cos3x|?
(2) The integral of x/(x^(2)-1)^2 --> not sure
(1) Substitute $u = \cos 3x$

(2) Substitute $u = x^2 - 1$

3. Originally Posted by Bure03
While doing some exercises in my cal II book i stumbled on these 2 questions.. Any help will be appreciated. Thanks

(1) The integral of tan3x --> -1/3ln|cos3x|?
(2) The integral of x/(x^(2)-1)^2 --> not sure
#1 $\int\tan(3x)\,dx=\int\frac{\sin(3x)}{\cos(3x)}\,dx$

Make the substitution $z=\cos(3x)$

#2 $\int\frac{x\,dx}{(x^2-1)^2}$

Make the substitution $z=x^2-1$

Try taking it from here.

Hope this makes sense!

4. Originally Posted by Bure03
While doing some exercises in my cal II book i stumbled on these 2 questions.. Any help will be appreciated. Thanks

(1) The integral of tan3x --> -1/3ln|cos3x|?
Yes, that's correct. It can also be written as $\frac{1}{3}\ln|\sec(3x)|$.

5. thanks guys just wanted to double check my answers.