What is the integral of ((x+1)e^{(x+ln(x))})/x ?

The integral of ((x+1)e^{(x+ln(x))})/x is e^xx+C

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integral of ((x+1)e^{(x+ln(x))})/x

\int \frac{( x + 1 ) e ^{(x + l n (x))}}{x} d x

e^{x} x + C

Solution steps

\int \frac{( x + 1 ) e ^{x + l n (x)}}{x} d x

Simplify

\frac{( x + 1 ) e ^{x + l n (x)}}{x} : e^{x} (x + 1)

= \int e^{x} (x + 1) d x

Apply Integration By Parts

: e^{x} (x + 1) - \int e^{x} d x

= e^{x} (x + 1) - \int e^{x} d x

\int e^{x} d x = e^{x}

= e^{x} (x + 1) - e^{x}

Simplify

e^{x} (x + 1) - e^{x} : e^{x} x

= e^{x} x

Add a constant to the solution

= e^{x} x + C

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What is the integral of ((x+1)e^{(x+ln(x))})/x ?
The integral of ((x+1)e^{(x+ln(x))})/x is e^xx+C