x ^ e -1 + e ^ x -1 x ^ e + e ^ x d x is equal to
Mathematics · JEE Main · NTA Exams — Integral Calculus
\(\int \frac{\mathbf{x}^{\mathbf{e}-1}+\mathbf{e}^{\mathbf{x}-1}}{\mathbf{x}^{\mathbf{e}}+\mathbf{e}^{\mathbf{x}}} d \mathbf{x}\) is equal to
- \(\frac{1}{e} \log \left(x^{e}-e^{x}\right)+c\)
- \(\frac{1}{e} \log \left[x^{e}+e^{x}\right]+c\)
- \(\frac{1}{e} \log \left(e^{x}-x^{e}\right)+c\)
- None of the above
Answer
(B) 1 e [x^ e +e^ x ]+c
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