What is the integral of x^2e^{8x} ?

The integral of x^2e^{8x} is 1/8 e^{8x}x^2-1/256 (8e^{8x}x-e^{8x})+C

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integral of x^2e^{8x}

\int x^{2} e^{8 x} d x

\frac{1}{8} e^{8 x} x^{2} - \frac{1}{256} (8 e^{8 x} x - e^{8 x}) + C

Solution steps

\int x^{2} e^{8 x} d x

Apply Integration By Parts

: \frac{1}{8} e^{8 x} x^{2} - \int \frac{1}{4} e^{8 x} x d x

= \frac{1}{8} e^{8 x} x^{2} - \int \frac{1}{4} e^{8 x} x d x

\int \frac{1}{4} e^{8 x} x d x = \frac{1}{256} (8 e^{8 x} x - e^{8 x})

= \frac{1}{8} e^{8 x} x^{2} - \frac{1}{256} (8 e^{8 x} x - e^{8 x})

Add a constant to the solution

= \frac{1}{8} e^{8 x} x^{2} - \frac{1}{256} (8 e^{8 x} x - e^{8 x}) + C

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What is the integral of x^2e^{8x} ?
The integral of x^2e^{8x} is 1/8 e^{8x}x^2-1/256 (8e^{8x}x-e^{8x})+C