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

1. sami-21

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

can i do partial fraction method?

3. agent0smith

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

4. sami-21

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. sami-21

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. deena123

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

@sami-21 i dont understand

8. mathsmind

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. mathsmind

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

okay thank you!

11. mathsmind

you're welcome

12. mathsmind

did u solve the problem?