Solve \int 18z^(3)e^(z)dz

Question

Evaluate the integral

18 z^{3} e^{z} - 54 z^{2} e^{z} + 108 z e^{z} - 108 e^{z} + C, C \in R

Evaluate

\int 18 z^{3} e^{z} d z

Use the property of integral \int k f (x) d x = k \int f (x) d x

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

Prepare for integration by parts

u = z^{3} d v = e^{z} d z

Calculate the derivative

More Steps

d u = 3 z^{2} d z d v = e^{z} d z

Evaluate the integral

More Steps

d u = 3 z^{2} d z v = e^{z}

Substitute u = z^{3} 、 v = e^{z} 、 d u = 3 z^{2} d z 、 d v = e^{z} d z for \int u d v = uv - \int v d u

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

Calculate

18 z^{3} e^{z} - 18 \times \int 3 z^{2} e^{z} d z

Evaluate the integral

More Steps

18 z^{3} e^{z} - 54 z^{2} e^{z} + 108 z e^{z} - 108 e^{z}

Solution

18 z^{3} e^{z} - 54 z^{2} e^{z} + 108 z e^{z} - 108 e^{z} + C, C \in R

Show Solution