If , . Then, for an arbitrary constant , the value of…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

I = \int \frac{e^x}{e^{4x} + e^{2x} + 1} dx

J = \int \frac{e^{-x}}{e^{-4x} + e^{-2x} + 1} dx

. Then, for an arbitrary constant

c

, the value of

J - I

equals (1)

\frac{1}{2} \log \left| \frac{e^{4x} - e^{2x} + 1}{e^{4x} + e^{2x} + 1} \right| + C

(2)

\frac{1}{2} \log \left| \frac{e^{2x} + e^x + 1}{e^{2x} - e^x + 1} \right| + C

(3)

\frac{1}{2} \log \left| \frac{e^{2x} - e^x + 1}{e^{2x} + e^x + 1} \right| + C

(4)

\frac{1}{2} \log \left| \frac{e^{4x} + e^{2x} + 1}{e^{4x} - e^{2x} + 1} \right| + C