What is the integral of x^2e^{10x} ?

The integral of x^2e^{10x} is 1/10 e^{10x}x^2-1/500 (10e^{10x}x-e^{10x})+C

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integral of x^2e^{10x}

\int x^{2} e^{10 x} d x

\frac{1}{10} e^{10 x} x^{2} - \frac{1}{500} (10 e^{10 x} x - e^{10 x}) + C

Solution steps

\int x^{2} e^{10 x} d x

Apply Integration By Parts

: \frac{1}{10} e^{10 x} x^{2} - \int \frac{1}{5} e^{10 x} x d x

= \frac{1}{10} e^{10 x} x^{2} - \int \frac{1}{5} e^{10 x} x d x

\int \frac{1}{5} e^{10 x} x d x = \frac{1}{500} (10 e^{10 x} x - e^{10 x})

= \frac{1}{10} e^{10 x} x^{2} - \frac{1}{500} (10 e^{10 x} x - e^{10 x})

Add a constant to the solution

= \frac{1}{10} e^{10 x} x^{2} - \frac{1}{500} (10 e^{10 x} x - e^{10 x}) + C

y = \frac{1 + x f ( x )}{x}

\frac{\partial}{\partial x} ((x - y)^{4})

\int \frac{8 + 7 x}{1 + x ^{2}} d x

f (x) = x^{2} - 2, at x = 0

\int \frac{2 x ^{3} - 4 x ^{2} + 18 x}{x ^{2} + 9} d x

What is the integral of x^2e^{10x} ?
The integral of x^2e^{10x} is 1/10 e^{10x}x^2-1/500 (10e^{10x}x-e^{10x})+C