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

The Correct Option is A

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.