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## Homework Statement

[itex]\int_1^2 \frac {e^x}{x}\,dx[/itex] Through the use of differentiation under the integral sign.

**2. The attempt at a solution**

Tried inputting a several times, each one resulting in another function without an elementary anti-derivative (example given below)

[itex]I(a)=\int_1^2 \frac {e^{-ax}}{x}\,dx[/itex]

[itex]I'(a)=\int_1^2 -e^{-ax}\,dx[/itex]

[itex]I'(a)=\frac {e^{-2a}}{a}-\frac {e^{-a}}{a}[/itex]

[itex]I(a)=\int \frac {e^{-2a}}{a}\,da-\int \frac {e^{-a}}{a}\,da[/itex]

Resulting in a non-elementary anti-derivative...

Other examples I've tried include:

- [itex]I(a)=\int_1^2 \frac {e^x*sin(ax)}{x}[/itex]
- Subsituting x for ln(b), resulting in [itex]\int_1^2 \frac {1}{b*ln(b)}\,db[/itex], then saying [itex]I(a)=\int_1^2 \frac {1-b^a}{b*ln(b)}\,db[/itex]