Challenge Problems:

\(\displaystyle \int^{b}_{a} \frac{e^{x /a} - e^{b /x}}{x} \ dx \)

\(\displaystyle \int^{1}_{0} \sqrt[3]{2x^{3}-3x^2-x+1} \ dx \)

EDIT: I don't like the second integral. It doesn't even make any sense unless you state that \(\displaystyle \sqrt[3]{2x^{3}-3x^2-x+1} \) is a real-valued function. Sorry. It's a bad problem.

\(\displaystyle \int^{b}_{a} \frac{e^{x /a} - e^{b /x}}{x} \ dx \)

\(\displaystyle \int^{1}_{0} \sqrt[3]{2x^{3}-3x^2-x+1} \ dx \)

EDIT: I don't like the second integral. It doesn't even make any sense unless you state that \(\displaystyle \sqrt[3]{2x^{3}-3x^2-x+1} \) is a real-valued function. Sorry. It's a bad problem.

**Moderator edit:**Approved Challenge question.
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