Improper Integral

[tandoorichicken]

How do I do
\int_{3}^{6} (5-x)^{\frac{-1}{3}} \,dx
?

I also need to know how to do
\lim_{t\rightarrow\infty} \int_{-t}^{t} \frac{x}{x^2 + 1} \,dx

[ahrkron]

You could do both by substitution. Try the second one first. Define
u=x^2+1.
What is du?

However, there is a hidden trick on the second one... draw the integrand as a function of x... can you tell its area from -t to t "by eye"?