What is the integral of x^2e^{20x} ?

The integral of x^2e^{20x} is 1/20 e^{20x}x^2-1/4000 (20e^{20x}x-e^{20x})+C

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integral of x^2e^{20x}

\int x^{2} e^{20 x} d x

\frac{1}{20} e^{20 x} x^{2} - \frac{1}{4000} (20 e^{20 x} x - e^{20 x}) + C

Solution steps

\int x^{2} e^{20 x} d x

Apply Integration By Parts

: \frac{1}{20} e^{20 x} x^{2} - \int \frac{1}{10} e^{20 x} x d x

= \frac{1}{20} e^{20 x} x^{2} - \int \frac{1}{10} e^{20 x} x d x

\int \frac{1}{10} e^{20 x} x d x = \frac{1}{4000} (20 e^{20 x} x - e^{20 x})

= \frac{1}{20} e^{20 x} x^{2} - \frac{1}{4000} (20 e^{20 x} x - e^{20 x})

Add a constant to the solution

= \frac{1}{20} e^{20 x} x^{2} - \frac{1}{4000} (20 e^{20 x} x - e^{20 x}) + C

n = 0 \sum \infty (x - 5)^{n}

f (x) = 2 π x

f (x) = x + 7, at x = 2

\frac{d}{d x} (\frac{7 x - 11}{x})

y^{^{'}} = 9 x e^{y}, y (0) = 0

What is the integral of x^2e^{20x} ?
The integral of x^2e^{20x} is 1/20 e^{20x}x^2-1/4000 (20e^{20x}x-e^{20x})+C