What is the integral of x^2e^{18x} ?

The integral of x^2e^{18x} is 1/18 e^{18x}x^2-1/2916 (18e^{18x}x-e^{18x})+C

Popular >

integral of x^2e^{18x}

\int x^{2} e^{18 x} d x

\frac{1}{18} e^{18 x} x^{2} - \frac{1}{2916} (18 e^{18 x} x - e^{18 x}) + C

Solution steps

\int x^{2} e^{18 x} d x

Apply Integration By Parts

: \frac{1}{18} e^{18 x} x^{2} - \int \frac{1}{9} e^{18 x} x d x

= \frac{1}{18} e^{18 x} x^{2} - \int \frac{1}{9} e^{18 x} x d x

\int \frac{1}{9} e^{18 x} x d x = \frac{1}{2916} (18 e^{18 x} x - e^{18 x})

= \frac{1}{18} e^{18 x} x^{2} - \frac{1}{2916} (18 e^{18 x} x - e^{18 x})

Add a constant to the solution

= \frac{1}{18} e^{18 x} x^{2} - \frac{1}{2916} (18 e^{18 x} x - e^{18 x}) + C

\int 4 x d x

x \to 4 lim (\frac{x ^{4} - 256}{x ^{3} - 64})

(1 + x^{2})^{- \frac{3}{2}}

\frac{d}{d x} (\frac{x ^{2} + 2 x - 2}{( x + 1 ) ^{2}})

f (x) = \frac{7}{x}, x = 1, x = 41

What is the integral of x^2e^{18x} ?
The integral of x^2e^{18x} is 1/18 e^{18x}x^2-1/2916 (18e^{18x}x-e^{18x})+C