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

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

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integral of x^2e^{bx}

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int e^{b x} \frac{2}{b} x d x = \frac{2}{b} (e^{b x} \frac{1}{b} x - e^{b x} \frac{1}{b ^{2}})

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

Add a constant to the solution

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

sin (t + π)

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

y = 9 e^{x} cos (x)

1 - x

\int \frac{1}{m ^{3} + m} d m

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