Question

INTEGRATE : x^3/(x^2+1)^2

Answer 1

\[\int\limits_{}^{}\frac{ x ^{3} }{ (x ^{2 }+1)^{2} }\]

Answer 2

I would probably use this substitution: \[x=\tan \theta\]

Answer 3

ok, let me try it

Answer 4

Substitute u for x^2 ?

Answer 5

uhmmm, i thought i was going to easily figure the tan theta, but i am stuck

Answer 6

Actually you could probably do x^2+1=u and that will be MUCH easier.

Answer 7

ok, let me try that here

Answer 8

\[u= x ^{2} + 1\]

Answer 9

\[du =2xdx\]
\[\frac{ 1 }{ 2 }du=xdx\]
from above
\[x ^{2}=u-1\]
\[\int\limits_{}^{}\frac{ u-1 }{ u ^{2} }\]

Answer 10

is this the correct pathway

Answer 11

You got it. =) I am only cringing a little bit when you don't include your dx's and du's on your integrals but overall you're totally right!

Answer 12

thank you very much, i will surely remember to add them!