Find the integral.
-$\int 11 x^{2} e^{\left(-4 x^{3}\right)} d x$
A) $\frac{11}{12} e^{\left(-4 x^{3}\right)}+C$
B) $-11 e^{\left(-4 x^{3}\right)}+C$
C) $12 e^{\left(-4 x^{3}\right)}+C$
D) $-\frac{11}{12} e^{\left(-4 x^{3}\right)}+C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = -4x^3 $, then $ du = -12x^2 dx $. Thus, $ dx = \frac{du}{-12x^2} $. Substituting, the integral becomes $-\frac{11}{12} \int e^u du$, which evaluates to $-\frac{11}{12} e^u + C$. Substituting back $ u = -4x^3 $, the result is $-\frac{11}{12} e^{-4x^3} + C$.

Find the Integral ∫11x2e(−4x3)dx\int 11 x^{2} e^{\left(-4 x^{3}\right)} d x∫11x2e(−4x3)dx A) 1112e(−4x3)+C\frac{11}{12} e^{\left(-4 x^{3}\right)}+C1211​e(−4x3)+C

Find the Integral $\int 11 x^{2} e^{\left(-4 x^{3}\right)} d x$ A) $\frac{11}{12} e^{\left(-4 x^{3}\right)}+C$