JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int\left( e ^{2 x }+2 e ^{ x }- e ^{- x }-1\right) e ^{\left( e ^{ x }+ e ^{- x }\right)} d x\) \(=g(x) e^{\left(e^{x}+e^{-x}\right)}+c,\) where \(c\) is a constant of integration, then \(g (0)\) is equal to
- A \(2\)
- B \(e^{2}\)
- C \(e\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(e ^{2 x }+2 e ^{ x }- e ^{- x }-1\) \(= e ^{ x }\left( e ^{ x }+1\right)- e ^{- x }\left( e ^{ x }+1\right)+ e ^{ x }\) \(=\left[\left( e ^{ x }+1\right)\left( e ^{ x }- e ^{- x }\right)+ e ^{ x }\right]\) so…
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