What is the integral `int x^2*e^(x^3) dx`

Tuesday, September 7, 2010

What is the integral $\displaystyle\int{{x}}^{{2}}\cdot{{e}}^{{{{x}}^{{3}}}}{\left.{d}{x}\right.}$

The integral
$\displaystyle\int{{x}}^{{2}}\cdot{{e}}^{{{{x}}^{{3}}}}{\left.{d}{x}\right.}$ has to be determined.

Substitute $\displaystyle{{x}}^{{3}}={y}$

$\displaystyle\frac{{\left.{d}{y}}}{{\left.{d}{x}}}={3}\cdot{{x}}^{{2}}$

$\displaystyle\Rightarrow\ldots$

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