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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫dx1  −  e2x\int \frac{{dx}}{{\sqrt {1\,\, - \,\,{e^{2x}}} }} is equal to
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Correct option: C
−log⁡  ∣e−x  +  e−2x−  1∣  +  c- \log \,\,\left| {{e^{ - x}}\,\, + \,\,\sqrt {{e^{ - 2x}} - \,\,1} } \right|\,\, + \,\,c
Option C (- \log \\,\left| {{{{e^{ - x}}}\\ + \\,\sqrt {{{{e^{ - 2x}}} - \\,\\1} } } \right|\\,\\ + \\,\c- \log \\,\left| {{{{e^{ - x}}}\\ + \\,\sqrt {{{{e^{ - 2x}}} - \\,\\1} } } \right|\\,\\ + \\,\c) is correct because it is the result of integrating the given expression using substitution.

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