What is the integral of e^xx^4 ?

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

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integral of e^xx^4

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

\frac{d}{d θ} (a^{2} \cdot sin^{2} (θ) + b^{2} \cdot cos^{2} (θ))

f (x) = sin^{11} (x)

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\frac{2 ln ( 2 x )}{2 - 3 x}

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