What is the integral of ((x-1))/(x^2)e^x ?

The integral of ((x-1))/(x^2)e^x is -(e^x(x-1))/x+e^x+C

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integral of ((x-1))/(x^2)e^x

\int \frac{( x - 1 )}{x ^{2}} e^{x} d x

- \frac{e ^{x} ( x - 1 )}{x} + e^{x} + C

Solution steps

\int \frac{x - 1}{x ^{2}} e^{x} d x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \int \frac{e ^{x} ( x - 1 )}{x ^{2}} d x

Apply Integration By Parts

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

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

= - \frac{e ^{x} ( x - 1 )}{x} - (- e^{x})

Simplify

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

Add a constant to the solution

= - \frac{e ^{x} ( x - 1 )}{x} + e^{x} + C

What is the integral of ((x-1))/(x^2)e^x ?
The integral of ((x-1))/(x^2)e^x is -(e^x(x-1))/x+e^x+C