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

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

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integral of 6x*e^{-2}x

integral

6 x \cdot e^{- 2} x

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

Solution steps

\int 6 x 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 xx d x

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

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

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Simplify

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

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

Add a constant to the solution

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

\frac{t ^{2}}{( 1 + t ^{2} )}

\frac{e ^{4} ln ( x ) - e ^{5} ln ( x )}{x ^{5}}

\frac{1 - x ^{4}}{1 - x}

\frac{( cos ^{3} ( x ) )}{sin ^{4} ( x )}

(t^{2})^{2}

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