What is the integral of x^2e^{15x} ?

The integral of x^2e^{15x} is 1/15 e^{15x}x^2-2/3375 (15e^{15x}x-e^{15x})+C

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integral of x^2e^{15x}

\int x^{2} e^{15 x} d x

\frac{1}{15} e^{15 x} x^{2} - \frac{2}{3375} (15 e^{15 x} x - e^{15 x}) + C

Solution steps

\int x^{2} e^{15 x} d x

Apply Integration By Parts

: \frac{1}{15} e^{15 x} x^{2} - \int \frac{2}{15} e^{15 x} x d x

= \frac{1}{15} e^{15 x} x^{2} - \int \frac{2}{15} e^{15 x} x d x

\int \frac{2}{15} e^{15 x} x d x = \frac{2}{3375} (15 e^{15 x} x - e^{15 x})

= \frac{1}{15} e^{15 x} x^{2} - \frac{2}{3375} (15 e^{15 x} x - e^{15 x})

Add a constant to the solution

= \frac{1}{15} e^{15 x} x^{2} - \frac{2}{3375} (15 e^{15 x} x - e^{15 x}) + C

\int (1 + 3 t) t^{2} d t

x \to \infty lim (x e^{- x})

\frac{d}{d x} (tan (0))

\frac{\partial}{\partial x} (y^{3})

in (sin (x))

What is the integral of x^2e^{15x} ?
The integral of x^2e^{15x} is 1/15 e^{15x}x^2-2/3375 (15e^{15x}x-e^{15x})+C