Question

hard problem :(

Answer 1

What's the problem?

Answer 2

evaulate (x^3e^x^2) / (x^2 + 1)^2 dx

Answer 3

integral right?

Answer 4

yep :(

Answer 5

\[(x ^{3}e ^{x ^{2}})/(x ^{2}+1)^{2}dx\] Look like this?

Answer 6

\[\Large \int \frac{x^3 e^{x^2}}{(x^2 + 1)^2} dx\]
rught?

Answer 7

ya @lgbasallote

Answer 8

do i do u-sub?

Answer 9

my first guess would have been u=x^2

Answer 10

my first guess was partial fractions

Answer 11

wat about integration by parts?

Answer 12

will follow too I guess, but I thought I could make it a bit easier with a substitution at first, so far, I didn't manage though *grins*.

Answer 13

actually....you *do* sub by x^2 first

Answer 14

yeh, I think I got it now

\[ u= x^2 \longrightarrow du=2xdx \]

In the numerator you have have this annoying x^3

\[x^2 \cdot x dx = u \frac{1}{2}du \]

Answer 15

yup

Answer 16

looks a bit messy but then, if I didn't make any careless mistakes as I usually do

\[ \frac{1}{2} \int \frac{ue^u }{(u+1)^2}\]

Answer 17

so now integral by parts

Answer 18

did you get the same @lgbasallote ?

Answer 19

ok, good.

Answer 20

\[\large \large \frac{\frac{1}{2}e^{x^2}}{1+x^2}+C\]

Answer 21

thx :D