Anti-derivative - I want to make sure I'm doing this right

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irishpump

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Oct 25, 2011
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I don't know what it is, but whenever I get problems that involve "e" I seem to panic. Anyway, here's the problem:

xe^(x^2)


So I figured I need to substitue so I made U=x^2 --> xe^U, I know that e^x is e^x as the anti-derivative, so I came up with 1/2x^2*e^(x^2). Is this correct? If so great, if not I appreciate any help. Like I said, these are the types of problems that scare me.
 
irishpump said:
I don't know what it is, but whenever I get problems that involve "e" I seem to panic. Anyway, here's the problem:

xe^(x^2)


So I figured I need to substitue so I made U=x^2 --> xe^U, I know that e^x is e^x as the anti-derivative, so I came up with 1/2x^2*e^(x^2). Is this correct? If so great, if not I appreciate any help. Like I said, these are the types of problems that scare me.
Click to expand...

Unfortunately, you are incorrect. A quick check to see if you found the right anti-derivative is to take the derivative of it. If it matches your original function, great!

Anyway back to your problem.

You are trying to find an anti-derivative of \(\displaystyle xe^{x^{2}}\)

e is just a number, like pi or 3 or whatever. When you take the derivative of \(\displaystyle e^x\) it is \(\displaystyle e^x\) because \(\displaystyle ln(e) = 1\)

Thats why \(\displaystyle \frac{d}{dx}(2^x)=2^xln(2)\). Similarly \(\displaystyle \frac{d}{dx}(e^x)=e^xln(e)=e^x\)

..... and i just noticed you got the answer, so I will stop here.... but i will still post the above, in case it helps you.

Also, don't forget that you are looking for the general anti-derivative. You must include a +c, where c is a constant.

\(\displaystyle \int \!(xe^{x^{2}}) \, \mathrm{d}x = \frac{e^{x^2}}{2}+C\)
 
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