What is the integral of x^2e^{1x} ?

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

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integral of x^2e^{1x}

\int x^{2} e^{1 x} d x

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

Solution steps

\int x^{2} e^{1 \cdot x} d x

Simplify

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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

e^{- 2 t} sin (t)

x \to a lim (\frac{3}{0})

\frac{20}{s ( s + 10 )}

\frac{- x ^{2} - 4}{( x ^{2} - 4 ) ^{2}}

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