Evaluate the following definite integral: `int_1^e(e^x)/x(1+x log x)dx`

Explanation

Take `I=int_{1}^{e} frac{e^{x}}{x}(1+x log x) d x .`
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I=int_{1}^{e}(frac{e^{x}}{x}+e^{x} log x) d x `
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Rightarrow I=int_{1}^{e} frac{e^{x}}{x} d x+int_{1}^{e} e^{x} log x d x`


By using Integrating by parts
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Rightarrow I=[log x e^{x}]_{1}^{e}-int_{1}^{e} e^{x} log x d x+int_{1}^{e} e^{x} log x d x `
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