Calculus Please Help??
posted by Robin on .
Evaluate the integral (3x^216x19)/(x^34x^23x+18)

Have you done the method of partial fractions yet?

Yes, I know how to get variables. I got b=8, c=1, and a=2, but I don't know how to get an integral as an answer. I need help integrating 2 other problems I will post as well, if you can help me.

1. (5x^2+10x12)/(x5)(x^2+4)
2. (8x28)/((x2)(x+9))
I know how to integrate, I just don't know how to get an integral, after finding a,b,c, and from that point 
So you were able to use partial fractions to decompose it to
8/(x3)^2 + 2/(x3) + 1/(x+2)
that was the hardest part, the rest is easy
isn't the integral of 8/(x3)^2 equal to 8/(x3) ?
as to the others, you should recognize the pattern of the derivative of a log function
recall that is y = ln (u)
then dy/dx = (du/dx) / ln (u)
so if we integrate
8/(x3)^2 + 1/(x+2) + 2/(x3)
we get
8/(x3) + ln(x+2) + 2ln(x3) + constant 
For your 2nd part,
did you get the partial fraction breakdown of
2x/(x^2+4)  3/(x5) from (5x^2 + 10x  12)/((x5)(x^2+4)) ?
then your integral would be
ln(x^2+4)  3ln(x5) + a constant
let me know what you get for your last question.