Question

$∫x^2e^{x^3}dx$ equals

• 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. $\frac{1}{3}e^{x^2}+C$

Answer 1

Answer: (A)

$\frac{1}{3}e^{x^3}+C$

Answer 2

The correct answer is A:$=\frac{1}{3}e^{x^3}+C$
Let $I=∫x^2e^{x^3}dx$
Also,let $x^3=t\,\,3x^2dx=dt$
$⇒I=\frac{1}{3}∫e^tdt$
$=\frac{1}{3}(e^t)+C$
$=\frac{1}{3}e^{x^3}+C$
Hence,the correct answer is A.