What is the integral of x^2e^{12x} ?

The integral of x^2e^{12x} is 1/12 e^{12x}x^2-1/864 (12e^{12x}x-e^{12x})+C

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integral of x^2e^{12x}

\int x^{2} e^{12 x} d x

\frac{1}{12} e^{12 x} x^{2} - \frac{1}{864} (12 e^{12 x} x - e^{12 x}) + C

Solution steps

\int x^{2} e^{12 x} d x

Apply Integration By Parts

= \frac{1}{12} e^{12 x} x^{2} - \int \frac{1}{6} e^{12 x} x d x

\int \frac{1}{6} e^{12 x} x d x = \frac{1}{864} (12 e^{12 x} x - e^{12 x})

= \frac{1}{12} e^{12 x} x^{2} - \frac{1}{864} (12 e^{12 x} x - e^{12 x})

Add a constant to the solution

= \frac{1}{12} e^{12 x} x^{2} - \frac{1}{864} (12 e^{12 x} x - e^{12 x}) + C

What is the integral of x^2e^{12x} ?
The integral of x^2e^{12x} is 1/12 e^{12x}x^2-1/864 (12e^{12x}x-e^{12x})+C