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

AP Calculus ABmediummcq1 pt

Which of the following equals $\int \frac{1}{x^2+2x+5}\,dx$ ?

A.

\frac{1}{2}\arctan\left(\frac{x+1}{2}\right)+C

B.

\arctan\left(\frac{x+1}{2}\right)+C

C.

\frac{1}{4}\arctan\left(\frac{x+1}{2}\right)+C

D.

\ln\left((x+1)^2+4\right)+C

Explanation

Core Concept

Complete the square: $x^2+2x+5=(x+1)^2+4$ . With $a=2$ , the integral is $\frac{1}{2}\arctan\frac{x+1}{2}+C$ .

Correct Answer

A $\frac{1}{2}\arctan\left(\frac{x+1}{2}\right)+C$

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