AP Calculus ABmediummcq1 pt

Which of the following equals x2+1x2dx\int \frac{x^2+1}{x^2}\,dx?

A.x1x+Cx-\frac{1}{x}+C
B.x+1x+Cx+\frac{1}{x}+C
C.11x2+C1-\frac{1}{x^2}+C
D.x1x2+Cx-\frac{1}{x^2}+C

Explanation

Core Concept

Rewrite as 1+x21+x^{-2} and integrate: x+x11=x1x+Cx+\frac{x^{-1}}{-1}=x-\frac{1}{x}+C.

Correct Answer

Ax1x+Cx-\frac{1}{x}+C

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