Question

I have some problem with integration techniques. how can you integrate e^(x^2)*x? I tried integration by parts but it does not work. Also I have a problem integrating (2+x^3)^(1/2)*x^2. Thanks!

Answer 1

For the first one, I think you want to try a u-substitution with u=x^2.
For the second, I think you should try a u-sub with u=2+x^3.

Answer 2

(S) x e^x^2 dx

if u = x^2 then du = 2x dx... dx = du/2x

we already have an "x" in the integral, we need a 2 in there without changing the value.. so multiply the whole thing by 2/2.

(1/2) (S) 2x e^x^2 dx

(1/2) e^x^2 +C

Answer 3

yeah as Quantum said, both can be integrated using substitution technique.

Answer 4

(S) (2+x^3)^(1/2)*x^2 dx

if u = 2+x^3 ; then du = 3x^2 we need a 3x^2 in the integral to work with; so multiply by 3/3 and just set the (1/3) outside.

(1/3) (S) 3x^2 (2+x^3)^1/2 dx

1 2(2+x^3)^(3/2) +C
-- -------------
3 3

(2/9) (2+x^3)^(3/2) + C looks about right...