What is the integral of (x^2-6x+2)*e^x ?

The integral of (x^2-6x+2)*e^x is e^xx^2-8e^xx+10e^x+C

Popular >

integral of (x^2-6x+2)*e^x

\int (x^{2} - 6 x + 2) \cdot e^{x} d x

e^{x} x^{2} - 8 e^{x} x + 10 e^{x} + C

Solution steps

\int (x^{2} - 6 x + 2) e^{x} d x

Apply Integration By Parts

: (x^{2} - 6 x + 2) e^{x} - \int (2 x - 6) e^{x} d x

= (x^{2} - 6 x + 2) e^{x} - \int (2 x - 6) e^{x} d x

\int (2 x - 6) e^{x} d x = 2 e^{x} x - 8 e^{x}

= (x^{2} - 6 x + 2) e^{x} - (2 e^{x} x - 8 e^{x})

Simplify

(x^{2} - 6 x + 2) e^{x} - (2 e^{x} x - 8 e^{x}) : e^{x} x^{2} - 8 e^{x} x + 10 e^{x}

= e^{x} x^{2} - 8 e^{x} x + 10 e^{x}

Add a constant to the solution

= e^{x} x^{2} - 8 e^{x} x + 10 e^{x} + C

\frac{\partial}{\partial x} (3 x^{3} + 2 y^{2})

\frac{4}{x}, \frac{4}{x ^{2}}, 5

\int 2 e^{5 x} d x

n = 0 \sum \infty 2^{n}

(- x^{2} - 2 x - 2)^{3}

What is the integral of (x^2-6x+2)*e^x ?
The integral of (x^2-6x+2)*e^x is e^xx^2-8e^xx+10e^x+C