Question

Integration help~

Answer 1

\[\Large \int \frac{x~dx}{3+\sqrt{x}}\]

Answer 2

i'm thinking multiply by the conjugate, did you try that?

Answer 3

Yup, got me to:
\[\Large \int~\frac{x(3-\sqrt{x})}{9-x}~dx\]

\[\Large \int~\frac{3x-x^{3/2}}{9-x}~dx\]

Answer 4

Not sure where to go now..

Answer 5

i was thinking we could split it up and use partial fractions, but i am doubting that now...

Answer 6

I tried a u-sub, but then that 3/2 power would be a problem, unless I'm overthinking it.

Answer 7

WolframAlpha says to do Substitution twice. First with u=root x, then do long division, the do substitution again with u=1/(u+3)

Those steps should help.

Answer 8

To me, I let u =3+x^(1/2) --> du = 1/2x^(1/2) dx
and x ^(1/2)=u-3 --> x = (u-3)^2
and from dx =2\(\sqrt x\)du replace x^1/2 = u -3
you have the outlet there

Answer 9

wolf usually doesn't have the best ways of doing things, though i'm sure that works

Answer 10

Yes use substitution 3 + sqrt(x) = u

Answer 11

yeah that works

Answer 12

Cool, good to know ^_^

Answer 13

Oh, alright, thanks guys :)

Answer 14

http://symbolab.com/solver/step_by_step/%5Cint%5Cfrac%7Bx%7D%7B3%2B%5Csqrt%7Bx%7D%7D%20dx/?origin=enterkey

Answer 15

U r welcome :)

Answer 16

Use this link its awesome