Antidifferentiation

**linlinrocks** · May 8th 2009, 07:42 PM

I was working on some new homework and I'm having a hard time antidifferentiating problems like these:

$\int_2^5 (3-(6/x))^2dx$

For this one, I tried multiplying it out and got

${\int _2^5 (9-36/x+36/x^2)}dx$
and tried to use that to find the integral, but I ran into the problem of having to differentiate $36/x^2$

Another problem that I can't do is
$x={\int_0^y\sqrt{9t^2+6t}dt}$ for when y is greater than or equal to 1 and less than or equal to 5.
On this problem, I have to find the length of the curve. I know the process, but I can't do it if I can't antidifferentiate that equation.

**Pinkk** · May 8th 2009, 08:57 PM

Do you mean you were having a problem finding the antiderivative of $\frac{36}{x^{2}}$ ?

$\int 36x^{-2}\,\,dx= \frac{36x^{-2+1}}{-1} = -\frac{36}{x}$ .

With your second problem, complete the square and use trig substitution.

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