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

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

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integral of 2e^{-2}x

integral

2 e^{- 2} x

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

Solution steps

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

Take the constant out:

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

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

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{2}{e ^{2}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{2}{e ^{2}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{e ^{2}}

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

Add a constant to the solution

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

3 x^{2} + 2 x + 1

\frac{( x ^{3} - x ^{2} + x - 1 )}{( x - 1 )}

\frac{1}{x ^{2} ( 2 x + 1 ) ^{3}}

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

(2 x - 1) e^{x}