What is the integral of xe^{-2.1x} ?

The integral of xe^{-2.1x} is 0.22675…(-2.1e^{-2.1x}x-e^{-2.1x})+C

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integral of xe^{-2.1x}

\int x e^{- 2.1 x} d x

0.22675 \dots (- 2.1 e^{- 2.1 x} x - e^{- 2.1 x}) + C

Solution steps

\int x e^{- 2.1 x} d x

Apply u-substitution

= \int \frac{10 e ^{u} u}{44.1} d u

Take the constant out:

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

= \frac{10}{44.1} \cdot \int e^{u} u d u

Simplify

= 0.22675 \dots \cdot \int e^{u} u d u

Apply Integration By Parts

= 0.22675 \dots (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= 0.22675 \dots (e^{u} u - e^{u})

Substitute back

u = - 2.1 x

= 0.22675 \dots (e^{- 2.1 x} (- 2.1 x) - e^{- 2.1 x})

Simplify

= 0.22675 \dots (- 2.1 e^{- 2.1 x} x - e^{- 2.1 x})

Add a constant to the solution

= 0.22675 \dots (- 2.1 e^{- 2.1 x} x - e^{- 2.1 x}) + C

What is the integral of xe^{-2.1x} ?
The integral of xe^{-2.1x} is 0.22675…(-2.1e^{-2.1x}x-e^{-2.1x})+C