Integrate \(5 x^{-1}+e^{2}\) with respect to \(x\).
A. \(-\mathrm{e}^{1}+x^{5}+k \quad\) B. e \(-x+x^{5}+k\) C. \(-\mathrm{e}^{-}-x^{-5}+k \quad\) D. \(-\mathrm{e}^{-x}+x^{-1}+k\)
Correct Answer: A
Explanation
\(5 x^{4}+e x\) to integrate \(\int\left(5 x^{4}+e^{-1}\right) d x\) We separate the integral i.e. \(=\int 5 x^{-4} d x+\int e^{-x} d x\) Then integrating. we obtain \begin{array}{l} =\frac{5 x^{-3+1}}{4+1}+\frac{e^{-r}}{(-1)}+k \\ =\frac{ ot 8 x^{5}}{ ot 8}-e^{-r}+k \\ \text { or }-e^{-1}+x^{5}+k \end{array}