What is the integral of (e^{3x})/(x^2) ?

The integral of (e^{3x})/(x^2) is -(e^{3x})/x+3\Ei(3x)+C

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integral of (e^{3x})/(x^2)

\int \frac{e ^{3 x}}{x ^{2}} d x

- \frac{e ^{3 x}}{x} + 3 Ei (3 x) + C

Solution steps

\int \frac{e ^{3 x}}{x ^{2}} d x

Apply Integration By Parts

: - \frac{e ^{3 x}}{x} - \int - \frac{3 e ^{3 x}}{x} d x

= - \frac{e ^{3 x}}{x} - \int - \frac{3 e ^{3 x}}{x} d x

\int - \frac{3 e ^{3 x}}{x} d x = - 3 Ei (3 x)

= - \frac{e ^{3 x}}{x} - (- 3 Ei (3 x))

Simplify

= - \frac{e ^{3 x}}{x} + 3 Ei (3 x)

Add a constant to the solution

= - \frac{e ^{3 x}}{x} + 3 Ei (3 x) + C

x \to 6 lim (\frac{1}{x ^{2} - 36})

(t - cos (t))^{^{'}}

x \to 0 lim (\frac{1}{1 + sin ( x )})

\frac{d h}{d t} = - h

\int \frac{4}{( 2 x + 1 ) ^{3}} d x

What is the integral of (e^{3x})/(x^2) ?
The integral of (e^{3x})/(x^2) is -(e^{3x})/x+3\Ei(3x)+C