find the antiderivative of x^2e^(3x)  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

find the antiderivative of x^2e^(3x)

Postby yabo2k on Thu May 07, 2009 1:06 am

find the antiderivative of x^2e^(3x)
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Re: find the antiderivative

Postby Martingale on Thu May 07, 2009 2:20 am

yabo2k wrote:find the antiderivative of x^2e^(3x)


use integration by parts
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Re: find the antiderivative of x^2e^(3x)

Postby yabo2k on Thu May 07, 2009 10:19 pm

i get ((x^2e^3x)/3)-((2xe^3x)/9)-((2e^3x)/9)+C
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Re: find the antiderivative of x^2e^(3x)

Postby Martingale on Thu May 07, 2009 11:00 pm

yabo2k wrote:i get ((x^2e^3x)/3)-((2xe^3x)/9)-((2e^3x)/9)+C


close...

look at the last bit...(2e^3x)/9
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Re: find the antiderivative of x^2e^(3x)

Postby yabo2k on Thu May 07, 2009 11:05 pm

would it be e^(3x)/3?
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Re: find the antiderivative of x^2e^(3x)

Postby Martingale on Thu May 07, 2009 11:06 pm

yabo2k wrote:would it be e^(3x)/3?


no
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Re: find the antiderivative of x^2e^(3x)

Postby Martingale on Thu May 07, 2009 11:13 pm

yabo2k wrote:find the antiderivative of x^2e^(3x)






Spoiler:












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Re: find the antiderivative of x^2e^(3x)

Postby yabo2k on Thu May 07, 2009 11:21 pm

I'll do it step by step

udv=(x^2)(e^3x/3)-(e^3x/3)(2xdx)

=(x^2e^3x)/3-(2xe^3x)dx/3)

Then do I need to find the antiderivative of the second part (2xe^3x)dx/3) because there are two fnc (2x/3) and (e^3x)

u= 2x/3 dv= (e^3x)dx
du= (2/3)dx v= (e^3x/3)

am I going in the right direction?
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Re: find the antiderivative of x^2e^(3x)

Postby Martingale on Thu May 07, 2009 11:24 pm

yabo2k wrote:I'll do it step by step

udv=(x^2)(e^3x/3)-(e^3x/3)(2xdx)

=(x^2e^3x)/3-(2xe^3x)dx/3)

Then do I need to find the antiderivative of the second part (2xe^3x)dx/3) because there are two fnc (2x/3) and (e^3x)

u= 2x/3 dv= (e^3x)dx
du= (2/3)dx v= (e^3x/3)

am I going in the right direction?

yes
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Re: find the antiderivative of x^2e^(3x)

Postby yabo2k on Thu May 07, 2009 11:33 pm

for the antiderivative of the second part then I would get

(2x/3)(e^3x/3)-(e^3x/3)((2/3)dx)
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