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

The integral of x^4e^{4x} is 1/4 e^{4x}x^4-1/256 (64e^{4x}x^3-3(16e^{4x}x^2-2(4e^{4x}x-e^{4x})))+C

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integral of x^4e^{4x}

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

\frac{1}{4} e^{4 x} x^{4} - \frac{1}{256} (64 e^{4 x} x^{3} - 3 (16 e^{4 x} x^{2} - 2 (4 e^{4 x} x - e^{4 x}))) + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{4} e^{4 x} x^{4} - \int e^{4 x} x^{3} d x

= \frac{1}{4} e^{4 x} x^{4} - \int e^{4 x} x^{3} d x

\int e^{4 x} x^{3} d x = \frac{1}{256} (64 e^{4 x} x^{3} - 3 (16 e^{4 x} x^{2} - 2 (4 e^{4 x} x - e^{4 x})))

= \frac{1}{4} e^{4 x} x^{4} - \frac{1}{256} (64 e^{4 x} x^{3} - 3 (16 e^{4 x} x^{2} - 2 (4 e^{4 x} x - e^{4 x})))

Add a constant to the solution

= \frac{1}{4} e^{4 x} x^{4} - \frac{1}{256} (64 e^{4 x} x^{3} - 3 (16 e^{4 x} x^{2} - 2 (4 e^{4 x} x - e^{4 x}))) + C

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What is the integral of x^4e^{4x} ?
The integral of x^4e^{4x} is 1/4 e^{4x}x^4-1/256 (64e^{4x}x^3-3(16e^{4x}x^2-2(4e^{4x}x-e^{4x})))+C