How do you integrate ∫exsin√xdx using integration by parts?

2 Answers
Gió
May 11, 2018

I got overenthusiastic but I got stuck....I am not sure about it...I suspect it is either very complicated or not possible directly...

Explanation:

I got stuck...

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Jarob R G.
May 11, 2018

You do not.

Explanation:

You are not going to find a satisfactory answer to this integral. That is, the result cannot be represented by elementary functions. For reference, an acceptable result of this integral would be:

∫(exsin(√x))dx=−(14)i(4√e√π erf(12−i√x)−4√e√π erf(12+i√x)+2ex−i√x(−1+e2i√x))+C

where erf(x)=2√π∫x0e−t2dt and i is the imaginary number.

You would not encounter this type of integral in a high school or college level calculus class. In fact, you would not see an integral of this type even while pursuing an undergraduate mathematics degree.

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