Question

integrate 2 / x(x^2+1)^2

Answer 1

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

Answer 2

can i do partial fraction method?

Answer 3

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

Answer 4

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 .

Answer 5

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

Answer 6

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

Answer 7

@sami-21 i dont understand

Answer 8

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...

Answer 9

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

Answer 10

okay thank you!

Answer 11

you're welcome

Answer 12

did u solve the problem?