What is the integral of 0.733xe^{-0.27x} ?

The integral of 0.733xe^{-0.27x} is 10.05486…(-0.27e^{-0.27x}x-e^{-0.27x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 0.733xe^{-0.27x}

\int 0.733 x e^{- 0.27 x} d x

10.05486 \dots (- 0.27 e^{- 0.27 x} x - e^{- 0.27 x}) + C

Solution steps

\int 0.733 x e^{- 0.27 x} d x

Take the constant out:

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

= 0.733 \cdot \int x e^{- 0.27 x} d x

Apply u-substitution

= 0.733 \cdot \int \frac{100 e ^{u} u}{7.29} d u

Take the constant out:

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

= 0.733 \cdot \frac{100}{7.29} \cdot \int e^{u} u d u

Simplify

= 0.733 \cdot 13.71742 \dots \cdot \int e^{u} u d u

Apply Integration By Parts

= 0.733 \cdot 13.71742 \dots (e^{u} u - \int e^{u} d u)

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

= 0.733 \cdot 13.71742 \dots (e^{u} u - e^{u})

Substitute back

u = - 0.27 x

= 0.733 \cdot 13.71742 \dots (e^{- 0.27 x} (- 0.27 x) - e^{- 0.27 x})

Simplify

= 10.05486 \dots (- 0.27 e^{- 0.27 x} x - e^{- 0.27 x})

Add a constant to the solution

= 10.05486 \dots (- 0.27 e^{- 0.27 x} x - e^{- 0.27 x}) + C

What is the integral of 0.733xe^{-0.27x} ?
The integral of 0.733xe^{-0.27x} is 10.05486…(-0.27e^{-0.27x}x-e^{-0.27x})+C