Homework Help: Calc II

Posted by Jenna on Sunday, December 6, 2009 at 10:08pm.

Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and evaluate the integral:
(integral of) 2y^4dy/y^3 - y^2 + y - 1
After long divison I get:
(integral of)2ydy + 2(integral of)dy + (integral of) 2/y^3 - y^2 + y - 1
I keep getting stuck here. I can't write this as a sum of partial fractions because I can't figure out how to rearrange the denominator so that I CAN write it as a sum o partial fractions. Any ideas?

Calc II - Reiny, Sunday, December 6, 2009 at 10:48pm
You can factor
y^3 - y^2 + y - 1
= y^2(y-1) + (y-1)
= (y-1)(y^2 + 1)

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