IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Light on February 06, 2010, 02:01:33 pm

Title: integration
Post by: Light on February 06, 2010, 02:01:33 pm: how to integrate by recognition: (7x^2)(x^3 +1)^5 dx ?
Title: Re: integration
Post by: astarmathsandphysics on February 06, 2010, 02:22:47 pm: Multiply the bracket out then integrate term by term using $\int Ax^n dx = \frac{Ax^{n+1}}{n+1}$
Title: Re: integration
Post by: Light 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.==
Title: Re: integration
Post by: astarmathsandphysics 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 $du=3x^2 dx$
$\int 7x^2(x^3+1)^5dx=\int 7/3 u*u^5du=\int 7/3 u^6du = 7/18 u^6 =7/18 (x^3+1)^6 +C$
Title: Re: integration
Post by: Light on February 06, 2010, 02:35:48 pm: but question says integration by recognition.
Title: Re: integration
Post by: astarmathsandphysics on February 06, 2010, 03:02:33 pm: I am surprised. Manipulation involved. See my answer above