Apentix/AP Calculus AB/Unit 6: Integration and Accumulation of Change/Question
AP Calculus ABmediummcq1 pt

Which of the following equals ∫x2(x3+1)4 dx\int x^2(x^3+1)^4\,dx?

A.(x3+1)515+C\frac{(x^3+1)^5}{15}+C
B.(x3+1)55+C\frac{(x^3+1)^5}{5}+C
C.(x3+1)5+C(x^3+1)^5+C
D.3(x3+1)55+C\frac{3(x^3+1)^5}{5}+C

Explanation

Core Concept

With u=x3+1u=x^3+1, du=3x2 dxdu=3x^2\,dx, so the integral is 13⋅u55=(x3+1)515+C\frac{1}{3}\cdot\frac{u^5}{5}=\frac{(x^3+1)^5}{15}+C.

Correct Answer

A(x3+1)515+C\frac{(x^3+1)^5}{15}+C

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