What is the integral of x^4*e^{12x} ?

The integral of x^4*e^{12x} is 1/12 e^{12x}x^4-1/10368 e^{12x}(288x^3-72x^2+12x-1)+C

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integral of x^4*e^{12x}

\int x^{4} \cdot e^{12 x} d x

\frac{1}{12} e^{12 x} x^{4} - \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1) + C

Solution steps

\int x^{4} e^{12 x} d x

Apply Integration By Parts

: \frac{1}{12} e^{12 x} x^{4} - \int \frac{1}{3} e^{12 x} x^{3} d x

= \frac{1}{12} e^{12 x} x^{4} - \int \frac{1}{3} e^{12 x} x^{3} d x

\int \frac{1}{3} e^{12 x} x^{3} d x = \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1)

= \frac{1}{12} e^{12 x} x^{4} - \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1)

Add a constant to the solution

= \frac{1}{12} e^{12 x} x^{4} - \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1) + C

2 x y^{^{'}} + y = 2 x

\frac{\partial}{\partial x} (x e^{x y})

y = x^{2} + 5 x + 3, at x = 1

\frac{d}{d x} (3 (5 - 7 x)^{5})

\frac{\partial}{\partial x} (x^{\frac{3}{4}} y^{- 4})

What is the integral of x^4*e^{12x} ?
The integral of x^4*e^{12x} is 1/12 e^{12x}x^4-1/10368 e^{12x}(288x^3-72x^2+12x-1)+C