What is the integral of x^4e^x ?

The integral of x^4e^x is x^4e^x-4(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C

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integral of x^4e^x

\int x^{4} e^{x} d x

x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

Solution steps

\int x^{4} e^{x} d x

Apply Integration By Parts

: x^{4} e^{x} - \int 4 x^{3} e^{x} d x

= x^{4} e^{x} - \int 4 x^{3} e^{x} d x

\int 4 x^{3} e^{x} d x = 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

= x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

Add a constant to the solution

= x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

n = 0 \sum \infty (x + 4)^{n}

7 x + 4, at a = 3

\frac{d}{d θ} (ln (θ))

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

\int ln (3 x + 4) d x

What is the integral of x^4e^x ?
The integral of x^4e^x is x^4e^x-4(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C