If $d\,\,\left[ {\,f\,\,\left( x \right)} \right] = {e^{\tan x}}\,\,{\sec ^2}\,\,x\,\,\;dx,\;\,\,{\rm{then}}\;\,\,f\left( x \right)$ is equal to

${e^{{{\sec }^2}x}}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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d\,\,\left[ {\,f\,\,\left( x \right)} \right] = {e^{\tan x}}\,\,{\sec ^2}\,\,x\,\,\;dx,\;\,\,\mathrm{then}\;\,\,f\left( x \right)

is equal to

View answer and explanation

Correct option: A

{e^{\tan x}}\,\, + \,\,c

Option A (e^{(tan x)} + c) is correct because it is the antiderivative of e^{(tan x)} * sec²(x), found by recognizing that sec²(x) is the derivative of tan(x).

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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