- #1

Office_Shredder

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## Main Question or Discussion Point

a.) Poor Wolfram Alpha got asked to calculate the following integral

[tex] \int_{0}^{\infty} e^{-ax} \frac{\sin(x)}{x} dx [/tex]

but couldn't handle it!

http://www.wolframalpha.com/input/?i=int_{0}^{infty}+e^{-ax}+sin(x)+/xdx

(Results are not guaranteed if you use wolfram alpha pro to spend more time calculating as I don't have that).

Prove that you're smarter than a computer and solve this integral for all a > 0.

b.) For reasons unknown, Wolfram Alpha can solve this exactly if a is an integer, but it won't tell the steps for how it solved it. As a side challenge, instead calculate the integral in a way that

Feel free to answer either a, b or a and b.

[tex] \int_{0}^{\infty} e^{-ax} \frac{\sin(x)}{x} dx [/tex]

but couldn't handle it!

http://www.wolframalpha.com/input/?i=int_{0}^{infty}+e^{-ax}+sin(x)+/xdx

(Results are not guaranteed if you use wolfram alpha pro to spend more time calculating as I don't have that).

Prove that you're smarter than a computer and solve this integral for all a > 0.

b.) For reasons unknown, Wolfram Alpha can solve this exactly if a is an integer, but it won't tell the steps for how it solved it. As a side challenge, instead calculate the integral in a way that

*only*works if a is an arbitrary positive or non-negative (your choice) integer.Feel free to answer either a, b or a and b.