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

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

Popular >

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

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

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

Solution steps

\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

= - \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

\int \frac{1}{3 cos ( x ) - 4 sin ( x )} d x

\frac{d ^{2}}{d x ^{2}} (\frac{e ^{x}}{x})

x \to - 3 - lim (\frac{∣ x + 3 ∣}{x + 3})

x \to - 8 - lim (\frac{x + 3}{x + 8})

\int_{0}^{1} 15 cos (x^{2}) d x

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