What is the integral of x^2e^{22x} ?

The integral of x^2e^{22x} is 1/22 e^{22x}x^2-1/5324 (22e^{22x}x-e^{22x})+C

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integral of x^2e^{22x}

\int x^{2} e^{22 x} d x

\frac{1}{22} e^{22 x} x^{2} - \frac{1}{5324} (22 e^{22 x} x - e^{22 x}) + C

Solution steps

\int x^{2} e^{22 x} d x

Apply Integration By Parts

= \frac{1}{22} e^{22 x} x^{2} - \int \frac{1}{11} e^{22 x} x d x

\int \frac{1}{11} e^{22 x} x d x = \frac{1}{5324} (22 e^{22 x} x - e^{22 x})

= \frac{1}{22} e^{22 x} x^{2} - \frac{1}{5324} (22 e^{22 x} x - e^{22 x})

Add a constant to the solution

= \frac{1}{22} e^{22 x} x^{2} - \frac{1}{5324} (22 e^{22 x} x - e^{22 x}) + C

What is the integral of x^2e^{22x} ?
The integral of x^2e^{22x} is 1/22 e^{22x}x^2-1/5324 (22e^{22x}x-e^{22x})+C