please help with an integral

Andi47 · 2009-05-13, 08:02

How do I integrate the following functions - I somehow don't see the trick...?

a.) integrate (2x² - 3x - 4) /(3x-5) dx

b.) integrate (4x² - 6x + 2)² * (3x - 5) / 2x³ dx

Batalov · 2009-05-13, 08:10

Hmm...
a. Divide, and you will get something like ax+b+c/(3x-5) which will become easy.
b. Probably, the easiest to do the same as a.

Mr. P-1 · 2009-05-13, 14:09

b: Multiply out the numerator and divide term by term by the denominator. The result will be a sum of +ve and -ve powers of x, plus a constant, which can be integrated term by term.

a. Do the substitution u = 3x - 5 then proceed as above.

Andi47 · 2009-05-13, 17:49

Quote:

Originally Posted by Mr. P-1

b: Multiply out the numerator and divide term by term by the denominator. The result will be a sum of +ve and -ve powers of x, plus a constant, which can be integrated term by term.

a. Do the substitution u = 3x - 5 then proceed as above.

Thanks! Seems I've been somewhat out of practice...

2009-05-13, 08:02	#1
Andi47 Oct 2004 Austria 9B2₁₆ Posts	please help with an integral How do I integrate the following functions - I somehow don't see the trick...? a.) integrate (2x² - 3x - 4) /(3x-5) dx b.) integrate (4x² - 6x + 2)² * (3x - 5) / 2x³ dx

2009-05-13, 14:09	#3
Mr. P-1 Jun 2003 10010010001₂ Posts	b: Multiply out the numerator and divide term by term by the denominator. The result will be a sum of +ve and -ve powers of x, plus a constant, which can be integrated term by term. a. Do the substitution u = 3x - 5 then proceed as above. Last fiddled with by Mr. P-1 on 2009-05-13 at 14:09

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2009-05-13, 08:10	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·11·457 Posts	Hmm... a. Divide, and you will get something like ax+b+c/(3x-5) which will become easy. b. Probably, the easiest to do the same as a.