Question:
\(∫x^2e^{x^3}dx\) equals
\(∫x^2e^{x^3}dx\) equals
Updated On: Sep 16, 2023
\(\frac{1}{3}e^{x^3}+C\)
\(\frac{1}{3}e^{x^2}+C\)
\(\frac{1}{2}e^{x^3}+C\)
\(\frac{1}{3}e^{x^2}+C\)
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The Correct Option is A
Solution and Explanation
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.
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.
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