Author Topic: integration  (Read 943 times)

Offline Light

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integration
« on: February 06, 2010, 02:01:33 pm »
how to integrate by recognition: (7x^2)(x^3 +1)^5 dx ?

Offline astarmathsandphysics

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Re: integration
« Reply #1 on: February 06, 2010, 02:22:47 pm »
Multiply the bracket out then integrate term by term using \int Ax^n dx = \frac{Ax^{n+1}}{n+1}
« Last Edit: February 06, 2010, 02:24:30 pm by astarmathsandphysics »

Offline Light

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Re: integration
« Reply #2 on: February 06, 2010, 02:30:02 pm »
but the answer is in form of factorised with power.is there any shorter way?power 5 need long way of expanding.==

Offline astarmathsandphysics

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Re: integration
« Reply #3 on: February 06, 2010, 02:34:49 pm »
I didn't see the power cos I was blinded by q80's link. Better then integration by substition

u=x^3+1
u=x^3 so du=3x^2 dx
\int 7x^2(x^3+1)^5dx=\int 7/3 u*u^5du=\int 7/3 u^6du = 7/18 u^6 =7/18 (x^3+1)^6 +C
« Last Edit: February 06, 2010, 03:01:37 pm by astarmathsandphysics »

Offline Light

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Re: integration
« Reply #4 on: February 06, 2010, 02:35:48 pm »
but question says integration  by recognition.

Offline astarmathsandphysics

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Re: integration
« Reply #5 on: February 06, 2010, 03:02:33 pm »
I am surprised. Manipulation involved. See my answer above