Calc easy
posted by Ang .
Having trouble getting the correct solution.
The integral of “x squared” in the numerator and “x squared plus x minus 6” in the denominator.
S X2 / (X2 + x – 6) dx
Thanks!
That's a messy one. According to my table of integrals.
The answer is
x/6 (1/72)loge(x^2 +x 6)
+ S dx/(x^2 +x 6)
and the last term is another integral that involves an arctangent.
I am not going to attempt to derive it.
Thanks for trying.
I do have the solution, but I'm stuck on part of ariving at the destination.
x  9/5 ln !x+3! + 4/5 ln !x2! + C
The trick may require using the method of partial fractions, whereby
x^2/[(x+3)(x2)] is rewritten as
1 + (6x)/(x+3)(x2)]
The "1" term will lead to the "x" term in the integral.
The technique of partial fractions is then applied to the (6x)/(x+3)(x2)] term, leaving you with two terms of the form
(ax + b)/(x + 3) + (cx + d)/(x2)
Do a search online or in your textbook on the method of parital fractions for additional help.
Thank you! Yes it was the algebraic partial fractions. YES!
Thanks again.
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