(Untitled)
I'm sorry if this question may seem elementary:
Calculate the integral of (x^3)(e^-(x^(2)))dx
I solved it as follows:
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u=x^2
du=2xdx
(1/2) Integral ue^-(u)du = (-1/2)(u^2/2)(e^-u) + C = (-1/4)(x^4)(e^-(x^(2))) + C.
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Online integrators tell me that the answer is (-1/2)e^-(x^(2))(x^2 + 1).
What am I doing wrong?
Calculate the integral of (x^3)(e^-(x^(2)))dx
I solved it as follows:
---
u=x^2
du=2xdx
(1/2) Integral ue^-(u)du = (-1/2)(u^2/2)(e^-u) + C = (-1/4)(x^4)(e^-(x^(2))) + C.
---
Online integrators tell me that the answer is (-1/2)e^-(x^(2))(x^2 + 1).
What am I doing wrong?
Comments 2
Integration by Parts
∫ u dv = u*v - ∫ v du
u = u
du = du
dv = e-u du
v = -e-u
(1/2)*[u*v - ∫ v du]
= (1/2) * [u*-e-u - ∫ -e-u du]
= (1/2) * [u*-e-u + ∫ e-u du]
= (1/2) * [u*-e-u -e-u]
= (-1/2)*(u+1)*e-u
f(x) = (-1/2)*(x2+1)*e-(x2) = Online Calc Answer
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