What is the integral of x^4e^{6x} ?

The integral of x^4e^{6x} is 1/6 e^{6x}x^4-1/324 e^{6x}(36x^3-18x^2+6x-1)+C

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integral of x^4e^{6x}

\int x^{4} e^{6 x} d x

\frac{1}{6} e^{6 x} x^{4} - \frac{1}{324} e^{6 x} (36 x^{3} - 18 x^{2} + 6 x - 1) + C

Solution steps

\int x^{4} e^{6 x} d x

Apply Integration By Parts

: \frac{1}{6} e^{6 x} x^{4} - \int \frac{2}{3} e^{6 x} x^{3} d x

= \frac{1}{6} e^{6 x} x^{4} - \int \frac{2}{3} e^{6 x} x^{3} d x

\int \frac{2}{3} e^{6 x} x^{3} d x = \frac{1}{324} e^{6 x} (36 x^{3} - 18 x^{2} + 6 x - 1)

= \frac{1}{6} e^{6 x} x^{4} - \frac{1}{324} e^{6 x} (36 x^{3} - 18 x^{2} + 6 x - 1)

Add a constant to the solution

= \frac{1}{6} e^{6 x} x^{4} - \frac{1}{324} e^{6 x} (36 x^{3} - 18 x^{2} + 6 x - 1) + C

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What is the integral of x^4e^{6x} ?
The integral of x^4e^{6x} is 1/6 e^{6x}x^4-1/324 e^{6x}(36x^3-18x^2+6x-1)+C