$\smallint \sqrt {{e^x} - \,\,1} \,dx$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \sqrt {{e^x} - \,\,1} \,dx

is equal to

View answer and explanation

Correct option: A

2\,\,\left[ {\sqrt {{e^x} - 1} - {{\tan }^{ - 1}}\,\,\sqrt {{e^x} - 1} } \right] + c

Option A is correct because the integral of

\sqrt{{e^x} - 1}

is found using substitution and trigonometric identities, resulting in

2[\sqrt{{e^x} - 1} - {\tan}^{ - 1}\,\sqrt{{e^x} - 1}] + c

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