$\int x^2e^{x^3}dx$

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int x^2e^{x^3}dx$

Options:

$3e^{x^3}+c$

$3e^{x^2}+c$

$\frac{e^{x^3}}{3}+c$

$\frac{e^{x^2}}{2}+c$

Correct Answer:

$\frac{e^{x^3}}{3}+c$

Explanation:

Put $x^3=t$

$ 3x^2 dx = dt \Rightarrow x^2 dx = \frac{dt}{3}$

$ I = \frac{1}{3} \int{e^t dt} = \frac{e^t}{3} + C= \frac{e^{x^3}}{3}+ C$