What is the integral of (x^2e^x)/((x+2)^2) ?

The integral of (x^2e^x)/((x+2)^2) is -(e^xx^2)/(x+2)+e^xx-e^x+C

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integral of (x^2e^x)/((x+2)^2)

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

- \frac{e ^{x} x ^{2}}{x + 2} + e^{x} x - e^{x} + C

Solution steps

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

Apply Integration By Parts

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

\int - e^{x} x d x = - e^{x} x + e^{x}

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

Simplify

= - \frac{e ^{x} x ^{2}}{x + 2} + e^{x} x - e^{x}

Add a constant to the solution

= - \frac{e ^{x} x ^{2}}{x + 2} + e^{x} x - e^{x} + C

\int - \frac{18}{x ^{19}} d x

\frac{d x}{d t} - \frac{x}{t - 1} = t^{2} + 2

x \to 0 lim (\frac{( 1 + x ) ^{2} - 1}{x})

y^{^{'}} = 1 + 9 x - 5 y

\int \frac{cos ( x )}{sin ^{4} ( x )} d x

What is the integral of (x^2e^x)/((x+2)^2) ?
The integral of (x^2e^x)/((x+2)^2) is -(e^xx^2)/(x+2)+e^xx-e^x+C