## shaqadry Group Title integrate 2 / x(x^2+1)^2 one year ago one year ago

1. sami-21 Group Title

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

can i do partial fraction method?

3. agent0smith Group Title

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

4. sami-21 Group Title

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 Group Title

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 Group Title

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

@sami-21 i dont understand

8. mathsmind Group Title

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 Group Title

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

okay thank you!

11. mathsmind Group Title

you're welcome

12. mathsmind Group Title

did u solve the problem?