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

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

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

integral

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

Ei (2 x) + C

Solution steps

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

(e^{x})^{2} = e^{2 x}

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

Apply u-substitution

: \int \frac{e ^{u}}{u} d u

= \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= Ei (u)

Substitute back

u = 2 x

= Ei (2 x)

Add a constant to the solution

= Ei (2 x) + C

- x^{2} ln (x)

\frac{x ^{2}}{x ^{2} + 1}

\frac{1}{( x ^{2} + 1 ) ^{3}}

y (4 - y)^{\frac{1}{2}}

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