What is the integral of x^2e^{6x} ?

The integral of x^2e^{6x} is 1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x})+C

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integral of x^2e^{6x}

\int x^{2} e^{6 x} d x

\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x}) + C

Solution steps

\int x^{2} e^{6 x} d x

Apply Integration By Parts

: \frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x

= \frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x

\int \frac{1}{3} e^{6 x} x d x = \frac{1}{108} (6 e^{6 x} x - e^{6 x})

= \frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})

Add a constant to the solution

= \frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x}) + C

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

\int x \cdot cos (4 x) d x

y^{^{'}} = y

\frac{4 - x ^{2}}{x ^{3}}

\frac{d}{d x} (sin (x) - x sin (y))

What is the integral of x^2e^{6x} ?
The integral of x^2e^{6x} is 1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x})+C