What is the integral of x^2e^{21x} ?

The integral of x^2e^{21x} is 1/21 e^{21x}x^2-2/9261 (21e^{21x}x-e^{21x})+C

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integral of x^2e^{21x}

\int x^{2} e^{21 x} d x

\frac{1}{21} e^{21 x} x^{2} - \frac{2}{9261} (21 e^{21 x} x - e^{21 x}) + C

Solution steps

\int x^{2} e^{21 x} d x

Apply Integration By Parts

: \frac{1}{21} e^{21 x} x^{2} - \int \frac{2}{21} e^{21 x} x d x

= \frac{1}{21} e^{21 x} x^{2} - \int \frac{2}{21} e^{21 x} x d x

\int \frac{2}{21} e^{21 x} x d x = \frac{2}{9261} (21 e^{21 x} x - e^{21 x})

= \frac{1}{21} e^{21 x} x^{2} - \frac{2}{9261} (21 e^{21 x} x - e^{21 x})

Add a constant to the solution

= \frac{1}{21} e^{21 x} x^{2} - \frac{2}{9261} (21 e^{21 x} x - e^{21 x}) + C

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What is the integral of x^2e^{21x} ?
The integral of x^2e^{21x} is 1/21 e^{21x}x^2-2/9261 (21e^{21x}x-e^{21x})+C