What is the integral of x^2e^{x+4} ?

The integral of x^2e^{x+4} is e^4(x^2e^x-2(e^xx-e^x))+C

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integral of x^2e^{x+4}

\int x^{2} e^{x + 4} d x

e^{4} (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

Solution steps

\int x^{2} e^{x + 4} d x

Simplify

e^{x + 4} : e^{x} e^{4}

= \int x^{2} e^{x} e^{4} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{4} \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

: x^{2} e^{x} - \int 2 x e^{x} d x

= e^{4} (x^{2} e^{x} - \int 2 x e^{x} d x)

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

= e^{4} (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= e^{4} (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

\int 1 + \frac{1}{y} d y

\int \frac{3 x}{( 4 - x ^{2} ) ^{3}} d x

e^{(2 t)}

\int \frac{1}{x ^{2} + 10 x} d x

\frac{d y}{d x} = - \frac{( e ^{x} )}{8}

What is the integral of x^2e^{x+4} ?
The integral of x^2e^{x+4} is e^4(x^2e^x-2(e^xx-e^x))+C