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anonymous

  • 5 years ago

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!

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  1. anonymous
    • 5 years ago
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    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.

  2. amistre64
    • 5 years ago
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    (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

  3. anonymous
    • 5 years ago
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    yeah as Quantum said, both can be integrated using substitution technique.

  4. amistre64
    • 5 years ago
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    (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...

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