AP Calculus ABmediummcq1 pt

What is the value of 012x(x2+1)3dx\int_0^1 2x(x^2+1)^3\,dx?

A.154\frac{15}{4}
B.14\frac{1}{4}
C.1515
D.44

Explanation

Core Concept

With u=x2+1u=x^2+1, du=2xdxdu=2x\,dx, and the bounds become u=1u=1 to u=2u=2. Then 12u3du=1614=154\int_1^2 u^3\,du=\frac{16-1}{4}=\frac{15}{4}.

Correct Answer

A154\frac{15}{4}

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