Question

$\int x^2 e^{x^3} d x$ is equal to

• A. $\frac{1}{3} e^{x^3}+C$
• B. $\frac{1}{3} e^{x^2}+C$
• C. $\frac{1}{2} e^{x^3}+C$
• D. $\frac{1}{2} e^{x^2}+C$

Answer 1

Answer: (A)

Let $I=\int x^2 e^{x^3} d x$
Put $x^3=t \Rightarrow 3 x^2=\frac{d t}{d x} \Rightarrow d x=\frac{d t}{3 x^2}$
$\therefore I=\frac{1}{3} \int e^t d t $
$\Rightarrow I=\frac{1}{3} e^t+C=\frac{1}{3} e^{x^3}+C$
Hence, correct option is (a).