Thread: Need help with an integral. Thanks in advance!

1. Need help with an integral. Thanks in advance!

I need help with this integral that was on an AP Calculus BC Practice Test.

$
\int_{1}^{e} \frac{ (x^2+1) } {x} dx

$

This is on the non-calculator section, so it doesn't need to be in decimal format - just simplified would be great.

Maybe even just give me a prod in the right direction as far as which method to use. I tried integration by parts, but got a different answer than what was provided in the five choices.

2. integral

Hello,

Do as follows:

$\int_{0}^{e} \frac{x^{2}+1}{x}dx=\int_{0}^{e}\left( \frac{x^{2}}{x}+\frac{1}{x} \right)dx=\int_{0}^{e}\left( x+\frac{1}{x} \right) dx=\left[\frac{1}{2}x^{2}+\ln|x|\right]_{0}^{e}$

Form here, simply insert the limits (the upper limit minus the lower limit).

3. Wow, that's a lot simpler than I was making it

Thank you so much!