- #1
TroyElliott
- 59
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Homework Statement
differentiate ∫ e^(-x*t^4)dt from -x to x with respect to x.[/B]
Homework Equations
erf(x) = (2/sqrt(π)) ∫e^(-t^2)dt from 0 to x.
Leibniz rule.
I know that ∫t^2e^(-t^2)dt from 0 to x = (√π/4)*erf(x) - (1/2)*x*e^(-x^2)[/B]
The Attempt at a Solution
By using Leibniz rule, I get d/dx ∫ e^(-x*t^4)dt from -x to x with respect to x is equal to e^(-x^5) + e^(-x^5) - ∫ t^(4)*e^(-x*t^4)dt from -x to x.
I am stuck on this integral above. Trying to think of a nice substitution to write the integral in terms of an error function.
Thanks for any tips![/B]
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