What is the integral of 21z^3e^z ?

The integral of 21z^3e^z is 21(z^3e^z-3(z^2e^z-2(e^zz-e^z)))+C

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integral of 21z^3e^z

\int 21 z^{3} e^{z} d z

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

Solution steps

\int 21 z^{3} e^{z} d z

Take the constant out:

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

= 21 \cdot \int z^{3} e^{z} d z

Apply Integration By Parts

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

= 21 (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}))

= 21 (z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z})))

Add a constant to the solution

= 21 (z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z}))) + C

\int_{0}^{2} y^{3} d y

\frac{1}{4 s}

\frac{\partial}{\partial x} (\frac{z}{y + z})

n = 0 \sum \infty (1 - x)^{n}

\frac{\partial}{\partial x} (ln (3 x + 6 y + 9 t))

What is the integral of 21z^3e^z ?
The integral of 21z^3e^z is 21(z^3e^z-3(z^2e^z-2(e^zz-e^z)))+C