Which substitution turns ∫ x^2e^x^3 dx into a standard form?

Indefinite Integrals · Question 18 of 90

Question 18

EasyOriginal question

Which substitution turns $\int x^2e^{x^3}\,dx$ into a standard form?

t = x^2

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t = e^x

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t = x^3

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t = x^2e^{x^3}

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CorrectNot quiteAnswer C

Correct answer: C

With $t = x^3$ , $dt = 3x^2\,dx$ , so $x^2\,dx = \frac{dt}{3}$ , which is the rest of the integrand.
The integral becomes $\frac{1}{3}\int e^t\,dt = \frac{1}{3}e^{x^3} + C$ .

Worth noting

Choose $t$ so that its derivative, up to a constant, is the factor left over.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.