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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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