What is the integral of x^2e^{17x} ?

The integral of x^2e^{17x} is 1/17 e^{17x}x^2-2/4913 (17e^{17x}x-e^{17x})+C

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integral of x^2e^{17x}

\int x^{2} e^{17 x} d x

\frac{1}{17} e^{17 x} x^{2} - \frac{2}{4913} (17 e^{17 x} x - e^{17 x}) + C

Solution steps

\int x^{2} e^{17 x} d x

Apply Integration By Parts

: \frac{1}{17} e^{17 x} x^{2} - \int \frac{2}{17} e^{17 x} x d x

= \frac{1}{17} e^{17 x} x^{2} - \int \frac{2}{17} e^{17 x} x d x

\int \frac{2}{17} e^{17 x} x d x = \frac{2}{4913} (17 e^{17 x} x - e^{17 x})

= \frac{1}{17} e^{17 x} x^{2} - \frac{2}{4913} (17 e^{17 x} x - e^{17 x})

Add a constant to the solution

= \frac{1}{17} e^{17 x} x^{2} - \frac{2}{4913} (17 e^{17 x} x - e^{17 x}) + C

\frac{1}{s - 5} e^{- s}

a x^{2} + ∣ x ∣^{3}

y^{^{'}} = \frac{- 1 + x + y}{1 + x}

\frac{9 - ln ( x )}{ln ( x ) - 1}

\int_{0}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

What is the integral of x^2e^{17x} ?
The integral of x^2e^{17x} is 1/17 e^{17x}x^2-2/4913 (17e^{17x}x-e^{17x})+C