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

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

A.x55+2x33+x+C\frac{x^5}{5}+\frac{2x^3}{3}+x+C
B.(x2+1)33+C\frac{(x^2+1)^3}{3}+C
C.x55+x33+x+C\frac{x^5}{5}+\frac{x^3}{3}+x+C
D.x55+2x33+C\frac{x^5}{5}+\frac{2x^3}{3}+C

Explanation

Core Concept

Expand: (x2+1)2=x4+2x2+1(x^2+1)^2=x^4+2x^2+1. Integrating gives x55+2x33+x+C\frac{x^5}{5}+\frac{2x^3}{3}+x+C.

Correct Answer

Ax55+2x33+x+C\frac{x^5}{5}+\frac{2x^3}{3}+x+C

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