Try integration by parts. http://www.slideshare.net/empoweringminds/integration-by-parts-tutorial-example-calculus-2How to evaluate this integral?
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Notice that 3x^2 is the derivative of x^3. That should give you a clue to the easy way to solve this one.
So the integral is just exp(x^3)?Notice that 3x^2 is the derivative of x^3. That should give you a clue to the easy way to solve this one.
Would integration by substitution be better?heathhosty,
Try integration by parts. http://www.slideshare.net/empoweringminds/integration-by-parts-tutorial-example-calculus-2
Ratch
Not quite. Watch out for the negative signs. You said it right above - "substitution". In particular, use \(u=-x^3\) which implies \( du=-3x^2 dx\).So the integral is just exp(x^3)?
Much better as it is a simpler technique to apply than integration by parts.Would integration by substitution be better?
Plus a constant...Not quite. Watch out for the negative signs. You said it right above - "substitution". In particular, use \(u=-x^3\) which implies \( du=-3x^2 dx\).
\( \int 3x^2e^{-x^3}dx=-\int e^u du=-e^u=-e^{-x^3} \)
Yes, indeed. I did not look at the problem close enough, and gave you bad advice. Substitution is the way to go on this one.Would integration by substitution be better?