What is the integral from 1 to 3 of 4xe^x ?

The integral from 1 to 3 of 4xe^x is 8e^3

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integral from 1 to 3 of 4xe^x

\int_{1}^{3} 4 x e^{x} d x

8 e^{3}

Decimal Notation

160.68429 \dots

Solution steps

\int_{1}^{3} 4 x e^{x} d x

Take the constant out:

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

= 4 \cdot \int_{1}^{3} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{1}^{3}

= 4 [e^{x} x - \int e^{x} d x]_{1}^{3}

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

= 4 [e^{x} x - e^{x}]_{1}^{3}

Compute the boundaries:

2 e^{3}

= 4 \cdot 2 e^{3}

Simplify

= 8 e^{3}

x \to 1 lim (π)

sin (π x)

t \to 0 lim (\frac{7}{1 + t})

\frac{\partial}{\partial y} (arctan (x + 8 y))

\frac{d}{d x} (\frac{1 - 3 x}{4 + x})

What is the integral from 1 to 3 of 4xe^x ?
The integral from 1 to 3 of 4xe^x is 8e^3