Question

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