Hey guys, I need some help on these questions:

http://i43.tinypic.com/63wyvc.jpg

Please help!

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- Jun 9th 2009, 04:49 PMhelp1Integration by partial fractions: HELP!
Hey guys, I need some help on these questions:

http://i43.tinypic.com/63wyvc.jpg

Please help! - Jun 9th 2009, 05:49 PMKaitosan
#55

(a.) Partial fractions

(b.) Partial fractions

(c.) Trigonometric substitution (use the "completing the square" operation)

As for #53, use polynomial division.

I don't understand #54 at all. - Jun 9th 2009, 05:53 PMapcalculus

For 53: You want to perform long division first, because the degree of the numerator is greater than that of the denominator.

for 54: a) You need a partial fraction with denominator for each k value between 1 and m. The same applies to part b)

For 55:

a) Multiply the numerator by 2 and divide by 2 before the integral sign. Note that the new numerator is the derivative of the denominator, so the resulting antiderivative is a one half times the logarithm of the denominator... plus a constant, of course.

b) partial fractions ... factor denominator, then split into fractions.

c) substitute

Good luck! - Jun 9th 2009, 07:15 PMSoroban
Hello, help1!

Quote:

53. What is the first step when integrating: .

Then integrate: .

Quote:

54. Describe the decomposition of the rational function

(a) if

Quote:

(b) if , where is irreducible.

. .