\(\int\displaystyle\frac{dx}{e^x+e^{-x}}\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\tan^{-1}(e^x)+c\): \(c\) is an arbitrary constant
Multiplying the numerator and the denominator by \(e^x\):
\( \displaystyle \int\frac{dx}{e^x + e^{-x}} = \int\frac{e^x\,dx}{e^{2x} + 1} \)
By the substitution \(t = e^x\), \(dt = e^x\,dx\), this becomes a standard integral:
\( \displaystyle \int\frac{dt}{t^2 + 1} = \tan^{-1}t + c \)
\( = \tan^{-1}(e^x) + c \)
NCERT (2026-27 edition):
Integrals
