Posted by **Jessica** on Monday, February 25, 2008 at 3:52am.

Calculate the integrals by partial fractions and using the indicated substitution. Show the results you get are the same.

dx/1-x^2; substitution x= sin pheta

I understand how to do the partial fraction part, but not the second part and I dont know how they are similar. Any help would be appreciated on what to do

- Math -
**drwls**, Monday, February 25, 2008 at 7:20am
They want you to do it two ways. The first is to change it to

dx/[2(1+x)] + dx/[2(1-x)]

which integrates to

(1/2)[ln(1+x) - ln(1-x)]

= (1/2)ln[(1+x)/(1-x)]

In the substitution method, with x = sin u

dx = cos u du

Integral dx/(1-x^2)= cos u du/1-sin^2u

= Integral du/cos u = Integral (sec u)

= (1/2)log[(1+sinu)/(1-sinu)]

= (1/2)log[(1+x)/(1-x)]

## Answer this Question

## Related Questions

- CALC 2 - Partial Functions!! - How do I solve Integral of 7/(16-x^2) I know I ...
- Math- Partial Fractions - Decompose the following into partial fractions after ...
- Calc easy - Having trouble getting the correct solution. The integral of “x ...
- Maths: Partial Differentiation - 1) If x = rcos theta and y = r sin theta, show ...
- partial fractions - (7x^2-16)/(x^2-2x) solve by using partial fraction ...
- Math Help - Directions: Decide whether the statements are true or false by using...
- Algebra-Partial Fractions - Can you please help me with the following questions ...
- Partial Decompostion Fractions - Can you please help me with the following ...
- Calculus - Integral of x sq/(1+x sq) dx I am not sure how to do this, am i ...
- calculus - Evaluate the following integrals using the given substitutions. (a) (...

More Related Questions