Evaluating a definite integral with e Consider the following problem, evaluate:
$$\int_0^1 \dfrac{x^2}{e^{2x^3}} dx$$
I tried the following method:
$\ln(x) = u$
$$\dfrac{1}{e^u} \cdot \dfrac{1}{6}du$$
$$\dfrac{1}{6} \cdot \ln(e^{2x^3}) + c$$
But if I use this I get incorrect answer. Where did I go wrong and what would I have to do to make correct use of this method to solve the problem?

Use $u=x^3$, then $dx = \frac{du}{3x^2}$. This turns the integral into:
$$\frac{1}{3}\int\limits_{0}^{1}e^{-2u}du = \frac{-1}{6}e^{-2u}+C=\frac{-1}{6}e^{-2x^3} +C$$
