What is the integral of 6e^{-2}x ?

The integral of 6e^{-2}x is (3x^2)/(e^2)+C

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integral of 6e^{-2}x

integral

6 e^{- 2} x

\frac{3 x ^{2}}{e ^{2}} + C

Solution steps

\int 6 e^{- 2} x d x

Take the constant out:

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

= 6 e^{- 2} \cdot \int x d x

6 e^{- 2} = \frac{6}{e ^{2}}

= \frac{6}{e ^{2}} \cdot \int x d x

Apply the Power Rule

= \frac{6}{e ^{2}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{6}{e ^{2}} \cdot \frac{x ^{2}}{2} : \frac{3 x ^{2}}{e ^{2}}

= \frac{3 x ^{2}}{e ^{2}}

Add a constant to the solution

= \frac{3 x ^{2}}{e ^{2}} + C