## anonymous 3 years ago integrate 2 / x(x^2+1)^2

1. anonymous

try substitution t=x^2 dt=2xdx 1/2dt=xdx

2. anonymous

can i do partial fraction method?

3. agent0smith

$\int\limits \frac{ 2 }{ x (x^2+1)^2} dx$ Hmm. Use partial fractions?

4. anonymous

yes you can use partial fraction . i guess fractions will be easy with linear terms so use t=x^2 dt=2xdx $\Large \int\limits \frac{dt}{t(t+1)^2}$ now use partial fractions .

5. anonymous

no we can write the original integral as $\Large \int\limits \frac{2xdx}{x^2(x^2+1)}$ so let t=x^2 dt=2xdx

6. anonymous

$2\left( \frac{ 1 }{ 2(x^2+1) }-\frac{ 1 }{ 2 }\log(x^2+1)+\log x \right)$

7. anonymous

@sami-21 i dont understand

8. anonymous

you can use partial fraction, this is because if the power of the denominator is greater than the power of the numerator that would be an alternative method...

9. anonymous

but for me personal i prefer the first method present by sami....

10. anonymous

okay thank you!

11. anonymous

you're welcome

12. anonymous

did u solve the problem?