What is the integral from ln(2) to 3 of (5e^x) ?

The integral from ln(2) to 3 of (5e^x) is 5(e^3-2)

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integral from ln(2) to 3 of (5e^x)

\int_{l n (2)}^{3} (5 e^{x}) d x

5 (e^{3} - 2)

Decimal Notation

90.42768 \dots

Solution steps

\int_{l n (2)}^{3} 5 e^{x} d x

Take the constant out:

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

= 5 \cdot \int_{l n (2)}^{3} e^{x} d x

Use the common integral:

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

= 5 [e^{x}]_{l n (2)}^{3}

Compute the boundaries:

e^{3} - 2

= 5 (e^{3} - 2)

x \to 2 lim (x - 3)

\int_{0}^{1} (x^{2} - x^{3}) d x

x \to 0 lim (\frac{1 - cos ( 7 x )}{4 x ^{2}})

\frac{d}{d x} (A (2 x e^{x} + e^{x} x^{2}))

x \to 2 lim (\frac{1}{2})

What is the integral from ln(2) to 3 of (5e^x) ?
The integral from ln(2) to 3 of (5e^x) is 5(e^3-2)