What is the integral of 7x^3e^x ?

The integral of 7x^3e^x is 7(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C

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integral of 7x^3e^x

\int 7 x^{3} e^{x} d x

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

Solution steps

\int 7 x^{3} e^{x} d x

Take the constant out:

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

= 7 \cdot \int x^{3} e^{x} d x

Apply Integration By Parts

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

= 7 (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}))

= 7 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

Add a constant to the solution

= 7 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

f (x) = x^{2} - 3 x + 4, at x = 1

\frac{d y}{d t} + 2 t y = 2 t e^{- t^{2}}

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

\int x^{6} - 4 x^{4} + x + 1 d x

\int \frac{t ^{5}}{t ^{2} + 10} d t

What is the integral of 7x^3e^x ?
The integral of 7x^3e^x is 7(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C