What is the integral of z^3e^z ?

The integral of z^3e^z is z^3e^z-3(z^2e^z-2(e^zz-e^z))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of z^3e^z

\int z^{3} e^{z} d z

z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z})) + C

Solution steps

\int z^{3} e^{z} d z

Apply Integration By Parts

: z^{3} e^{z} - \int 3 z^{2} e^{z} d z

= z^{3} e^{z} - \int 3 z^{2} e^{z} d z

\int 3 z^{2} e^{z} d z = 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z}))

= z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z}))

Add a constant to the solution

= z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z})) + C

\frac{d}{d x} (arctan (ln (x^{2})))

\frac{d}{d x} (ln (2 x))

\int \frac{8}{x + 1} d x

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

\frac{10}{s ( s + 2 ) ( s + 3 ) ^{2}}

What is the integral of z^3e^z ?
The integral of z^3e^z is z^3e^z-3(z^2e^z-2(e^zz-e^z))+C