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## Homework Statement

“Fun Homework Problem” assigned for extra credit...

∫ 0 to ∞ [(e^-x)-(e^-3x)]/x dx

**2. Homework Equations (supplied hints)**

I can get an abstract answer from wolfram but it’s not how the professor wants us to do it.

He gave us a couple “hints”; try to introduce a second variable and reverse the boundries

for example: ∫∫ f(y) f(x) dy dx? I’m assuming he means integrate with respect to y first.

A second possible hint was to try to get to ∫ 1/x dx by getting -[(e^-x)-(e^-3x)] on top to cancel the other.

## The Attempt at a Solution

The biggest problem I’m running into is the x on the bottom.

Can I set new boundries by introducing 1 to y+1? I feel like the only way to do this problem is by getting +n in the denominator in order to prevent division by 0 when evaluating 0 to infinity.

I’ve also tried multipling by x/x in order to get an x^2 and move it to the top but the following integration by parts seems to get me no where.

Is there a trig sub I’m not seeing?

Even my professor admits he’s having trouble with it, but “knows” it’s possible.

Thanks for any help...