What is the integral of x^2e^{16x} ?

The integral of x^2e^{16x} is 1/16 e^{16x}x^2-1/2048 (16e^{16x}x-e^{16x})+C

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integral of x^2e^{16x}

\int x^{2} e^{16 x} d x

\frac{1}{16} e^{16 x} x^{2} - \frac{1}{2048} (16 e^{16 x} x - e^{16 x}) + C

Solution steps

\int x^{2} e^{16 x} d x

Apply Integration By Parts

: \frac{1}{16} e^{16 x} x^{2} - \int \frac{1}{8} e^{16 x} x d x

= \frac{1}{16} e^{16 x} x^{2} - \int \frac{1}{8} e^{16 x} x d x

\int \frac{1}{8} e^{16 x} x d x = \frac{1}{2048} (16 e^{16 x} x - e^{16 x})

= \frac{1}{16} e^{16 x} x^{2} - \frac{1}{2048} (16 e^{16 x} x - e^{16 x})

Add a constant to the solution

= \frac{1}{16} e^{16 x} x^{2} - \frac{1}{2048} (16 e^{16 x} x - e^{16 x}) + C

\frac{d}{d x} (\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}})

\frac{3}{2} sin (x)

\frac{1}{x}, 1, 5

\int (2 y) d y

y = (\frac{1}{3})^{x}

What is the integral of x^2e^{16x} ?
The integral of x^2e^{16x} is 1/16 e^{16x}x^2-1/2048 (16e^{16x}x-e^{16x})+C