What is the integral of x^2e^{19x} ?

The integral of x^2e^{19x} is 1/19 e^{19x}x^2-2/6859 (19e^{19x}x-e^{19x})+C

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integral of x^2e^{19x}

\int x^{2} e^{19 x} d x

\frac{1}{19} e^{19 x} x^{2} - \frac{2}{6859} (19 e^{19 x} x - e^{19 x}) + C

Solution steps

\int x^{2} e^{19 x} d x

Apply Integration By Parts

: \frac{1}{19} e^{19 x} x^{2} - \int \frac{2}{19} e^{19 x} x d x

= \frac{1}{19} e^{19 x} x^{2} - \int \frac{2}{19} e^{19 x} x d x

\int \frac{2}{19} e^{19 x} x d x = \frac{2}{6859} (19 e^{19 x} x - e^{19 x})

= \frac{1}{19} e^{19 x} x^{2} - \frac{2}{6859} (19 e^{19 x} x - e^{19 x})

Add a constant to the solution

= \frac{1}{19} e^{19 x} x^{2} - \frac{2}{6859} (19 e^{19 x} x - e^{19 x}) + C

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\int \frac{x ^{3} + 27}{x + 3} d x

What is the integral of x^2e^{19x} ?
The integral of x^2e^{19x} is 1/19 e^{19x}x^2-2/6859 (19e^{19x}x-e^{19x})+C