# Improper Integral

1. Apr 1, 2004

### tandoorichicken

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

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

Last edited: Apr 1, 2004
2. Apr 1, 2004

### ahrkron

Staff Emeritus
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"?