What is the integral of (e^x)/(x^4) ?

The integral of (e^x)/(x^4) is -(e^x}{3x^3}+1/3 (-(e^x)/(2x^2)+1/2 (-\frac{e^x)/x+\Ei(x)))+C

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integral of (e^x)/(x^4)

\int \frac{e ^{x}}{x ^{4}} d x

- \frac{e ^{x}}{3 x ^{3}} + \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x))) + C

Solution steps

\int \frac{e ^{x}}{x ^{4}} d x

Apply Integration By Parts

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

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

\int - \frac{e ^{x}}{3 x ^{3}} d x = - \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x)))

= - \frac{e ^{x}}{3 x ^{3}} - (- \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x))))

Simplify

= - \frac{e ^{x}}{3 x ^{3}} + \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x)))

Add a constant to the solution

= - \frac{e ^{x}}{3 x ^{3}} + \frac{1}{3} (- \frac{e ^{x}}{2 x ^{2}} + \frac{1}{2} (- \frac{e ^{x}}{x} + Ei (x))) + C

y^{^{'}} - 5 y = 2 x^{2} - 5 x + 8

\frac{d}{d x} (- x^{3} + 20 x^{2} + 21 x)

y^{^{''}} + 4 y = x^{2}

y^{^{'}} = \frac{3 x}{y}

\frac{d}{d x} (\frac{ln ( 3 x ^{2} - 6 x )}{4 x ^{3} - 2})

What is the integral of (e^x)/(x^4) ?
The integral of (e^x)/(x^4) is -(e^x}{3x^3}+1/3 (-(e^x)/(2x^2)+1/2 (-\frac{e^x)/x+\Ei(x)))+C