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

AP Calculus ABhardmcq1 pt

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

A.

e^x+2x-e^{-x}+C

B.

e^x+2x+e^{-x}+C

C.

e^x+2+e^{-x}+C

D.

\ln(e^{2x}+2e^x+1)+C

Explanation

Core Concept

Divide each term by $e^x$ to get $e^x+2+e^{-x}$ . Integrating gives $e^x+2x-e^{-x}+C$ .

Correct Answer

A $e^x+2x-e^{-x}+C$

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