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Indefinite Integrals question

2008 · Shift 2 · Q33

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PYQ Library
JEE Advanced
Mathematics
Indefinite Integrals
2008 · Shift 2 · Q33

Indefinite Integrals question

2008 · Shift 2 · Q33

JEE AdvancedMathematicsIndefinite IntegralsMCQ+3 / −1

Let

I = \int {{{{e^x}} \over {{e^{4x}} + {e^{2x}} + 1}}dx,\,\,J = \int {{{{e^{ - x}}} \over {{e^{ - 4x}} + {e^{ - 2x}} + 1}}dx.} }

Then for an arbitrary constant

C

, the value of

J -I

equals :

A
${1 \over 2}\log \left( {{{{e^{4x}} - {e^{2x}} + 1} \over {{e^{4x}} + {e^{2x}} + 1}}} \right) + C$
B
${1 \over 2}\log \left( {{{{e^{2x}} + {e^x} + 1} \over {{e^{2x}} - {e^x} + 1}}} \right) + C$
C
${1 \over 2}\log \left( {{{{e^{2x}} - {e^x} + 1} \over {{e^{2x}} + {e^x} + 1}}} \right) + C$
D
${1 \over 2}\log \left( {{{{e^{4x}} + {e^{2x}} + 1} \over {{e^{4x}} - {e^{2x}} + 1}}} \right) + C$

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