[TI-M] Re: An Integral, hehehe
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[TI-M] Re: An Integral, hehehe
> (5+x^2)/(9-x^3) = (5a - 3) / 9(a - x) + ((5a - 6)x + (10a^2 - 3a)) / 9(a^2
+
> ax + x^2)
> = (5a - 3) / 9(a - x) + (2x + a)(2.5a - 3) / 9(a^2 + ax + x^2) + 7.5a /
> 9((x + a/2)^2 + (3/4)a^2)
>
> Integrating each part gives:
>
> (1/9) * ((3 - 5a) ln abs (a - x) + (2.5a - 3) ln (a^2 + ax + x^2) + 5a
> sqrt(3) / a * arctan((2x + a) / (a sqrt(3)))
Your parenthesis aren't balanced, and when I make my best guess at fixing it
and then try plugging in different values for x, it gives different results
than the calc's answer. And the difference between them isn't a constant,
either.
Furthermore, when I try integrating the expression you integrated, I get a
non-real result which is nothing like what you got. And unless you can
explain how to integrate that by hand, it's still not a satisfactory answer,
because you're still relying on the calc. It doesn't look like an easy one
to do by hand, either.
-Scott