What is the integral of x^2e^{3x} ?

The integral of x^2e^{3x} is 1/3 e^{3x}x^2-2/27 (3e^{3x}x-e^{3x})+C

Popular >

integral of x^2e^{3x}

\int x^{2} e^{3 x} d x

\frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x}) + C

Solution steps

\int x^{2} e^{3 x} d x

Apply Integration By Parts

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

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

\int \frac{2}{3} e^{3 x} x d x = \frac{2}{27} (3 e^{3 x} x - e^{3 x})

= \frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x})

Add a constant to the solution

= \frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x}) + C

f (x) = \frac{1}{5 + x ^{2}}, at x = 2

\int cot^{5} (x) csc (x) d x

\int \frac{x ^{2} - x + 28}{x ^{3} + 7 x} d x

\int \frac{- 2 x ^{2} + 8 x - 20}{x ^{2} - 4 x + 8} d x

What is the integral of x^2e^{3x} ?
The integral of x^2e^{3x} is 1/3 e^{3x}x^2-2/27 (3e^{3x}x-e^{3x})+C