What is the integral of 19x^3e^x ?

The integral of 19x^3e^x is 19(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C

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integral of 19x^3e^x

\int 19 x^{3} e^{x} d x

19 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

Solution steps

\int 19 x^{3} e^{x} d x

Take the constant out:

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

= 19 \cdot \int x^{3} e^{x} d x

Apply Integration By Parts

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

= 19 (x^{3} e^{x} - \int 3 x^{2} e^{x} d x)

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

= 19 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

Add a constant to the solution

= 19 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

\frac{\partial}{\partial y} (3 y^{2} + 10 x^{2} y^{2})

\frac{4}{1 + x ^{2}}

\frac{d}{d x} (\frac{1}{e})

\int \frac{1}{( e ^{2 x} + 4 )} d x

\frac{\partial}{\partial y} (2 x y + y^{4})

What is the integral of 19x^3e^x ?
The integral of 19x^3e^x is 19(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C