# Math Help - Improper Integral Help

1. ## Improper Integral Help

I am just starting on the improper integral section. I am having trouble with this problem because I cannot seem to break it down easily into something that does not have (x-5) in the denominator. If I try to do lim R -> 5+, I will still get an undefined answer. I am doing something wrong, but I do not know what.

12. $\int^6_5 \frac{dx}{(x-5)^{3/2}}$

I get the general antiderivative, but I cannot get rid of the denominator, and since the numerator is just 1, I cannot use L'Hopital's Rule.
2. Using the substitution $t=x-5$
$\displaystyle\int_5^6\dfrac{dx}{(x-5)^{3/2}}=\displaystyle\int_0^1\dfrac{dt}{t^{3/2}}=\displaystyle\lim_{ \epsilon \to 0^+}{\displaystyle\int_{\epsilon}^{ 1}\dfrac{dt}{t^{3/2}}}=\displaystyle\lim_{ \epsilon \to 0^+}\left[-\dfrac{2}{\sqrt{t}}\right]_{\epsilon}^1=\ldots$