Author Topic: integration (Read 1062 times)

Light · « **on:** February 06, 2010, 02:01:33 pm »

how to integrate by recognition: (7x^2)(x^3 +1)^5 dx ?

astarmathsandphysics · « **Reply #1 on:** February 06, 2010, 02:22:47 pm »

Multiply the bracket out then integrate term by term using $\int Ax^n dx = \frac{Ax^{n+1}}{n+1}$

Light · « **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.==

astarmathsandphysics · « **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 $du=3x^2 dx$
$\int 7x^2(x^3+1)^5dx=\int 7/3 u*u^5du=\int 7/3 u^6du = 7/18 u^6 =7/18 (x^3+1)^6 +C$

Light · « **Reply #4 on:** February 06, 2010, 02:35:48 pm »

but question says integration by recognition.

astarmathsandphysics · « **Reply #5 on:** February 06, 2010, 03:02:33 pm »

I am surprised. Manipulation involved. See my answer above

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Author Topic: integration (Read 1062 times)

Light

integration

astarmathsandphysics

Re: integration

Light

Re: integration

astarmathsandphysics

Re: integration

Light

Re: integration

astarmathsandphysics

Re: integration