What is the integral of (x^2)e^(x^3)?

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2007-07-13 18:15:32 · 3 answers · asked by Mommy in Cali 1 in Science & Mathematics ➔ Mathematics

I = ∫ x² e^(x³) dx
let u = x³
du = 3 x² dx
du / 3 = x² dx
I = (1/3) ∫ (e^u) du
I = (1/3) e^u + C
I = (1/3) e^(x³) + C

2007-07-13 19:19:02 · answer #1 · answered by Como 7 · 0⤊ 0⤋

This one is relatively easy... note that 3x^2 is the derivative of x^3. So the integral is (1/3)e^(x^3).

2007-07-14 01:23:01 · answer #2 · answered by Vince 2 · 0⤊ 0⤋

â«x^2e^(x^3) dx
= â«(1/3)e^(x^3) dx^3, since x^2dx = (1/3)dx^3
= (1/3)e^(x^3) + c

2007-07-14 01:23:47 · answer #3 · answered by sahsjing 7 · 0⤊ 0⤋