What is the integral of 11z^3e^z ?

The integral of 11z^3e^z is 11(z^3e^z-3(z^2e^z-2(e^zz-e^z)))+C

Popular >

integral of 11z^3e^z

\int 11 z^{3} e^{z} d z

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

Solution steps

\int 11 z^{3} e^{z} d z

Take the constant out:

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

= 11 \cdot \int z^{3} e^{z} d z

Apply Integration By Parts

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

= 11 (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}))

= 11 (z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z})))

Add a constant to the solution

= 11 (z^{3} e^{z} - 3 (z^{2} e^{z} - 2 (e^{z} z - e^{z}))) + C

2 e^{\frac{t}{2}}

\int_{0}^{1} y 1 - y^{2} d y

y = arctan (1) - x^{1} + x

\int_{2}^{t} \frac{1}{( 5 x ^{5} )} d x

\int \frac{tan ^{3} ( ln ( x ) )}{6 x} d x

What is the integral of 11z^3e^z ?
The integral of 11z^3e^z is 11(z^3e^z-3(z^2e^z-2(e^zz-e^z)))+C