What is the integral of-2e^xx^3 ?

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

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integral of-2e^xx^3

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

= - 2 (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}))

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

Add a constant to the solution

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

\frac{1}{x ^{11}}

(y^{3} + 7)^{6}

y = 9 + 8 x + 5 x e^{x}

\int 6 - ∣ x ∣ d x

y = - x^{2} + 16, y = \frac{- 1}{4} x - 1, y = x - 6.6

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