# Math - Indefinite Integration

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Use integration by parts to solve:

I = f (x^3)(e^(x^2)) dx

(Let "f" represent the integral)

Let u = (e^(x^2)), dx = (1) / (2x(e^(x^2))) du

Let dv = x^3, v = (x^4) / (4)

I = (1/4)(x^4)(e^(x^2)) - (1/4) f (x^3) (2(e^(x^2))) du

... and now I don't know what to do. I don't know how to take the antiderivative of (e^(x^2)).

• Math - Indefinite Integration -

You chose the wrong parts to break it up into. The integral of e^x^2 cannot be written in closed form. Use the fact that 2x e^x^2 is the derivative of e^x^2, and choose du = x e^x^2 dx,
u = (1/2)e^x^2
v = x^2
dv = 2x

The answer can be found at
http://www.karakas-online.de/forum/viewtopic.php?t=9515

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