Thursday

August 21, 2014

August 21, 2014

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

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 7:20amThey 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)]

**Related Questions**

calculus - Evaluate the following integrals using the given substitutions. (a) (...

Calculus - s=dx/(4+5cos x). By using t-substitution, i.e. t=tan(x/2) we get ...

Calculus 2 - Evalute the integral of x/(x^2+4)dx using u-substitution and then ...

Calculus - I have two questions, because I'm preparing for a math test on monday...

calculus - We're doing indefinite integrals using the substitution rule right ...

CALC 2 - Partial Functions!! - How do I solve Integral of 7/(16-x^2) I know I ...

calculus - Integrate x/(x^2 + 4) dx via trig substitution and by u=x^2+4 ...

calculus - Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = ...

Math- Partial Fractions - Decompose the following into partial fractions after ...

calc - find integral using table of integrals ) integral sin^4xdx this the ...