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

The integral of ((2e^x))/x is 2\Ei(x)+C

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

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

2 Ei (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{e ^{x}}{x} d x

Use the nonelementary integral:

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

= 2 Ei (x)

Add a constant to the solution

= 2 Ei (x) + C