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

The integral from ln(3) to ln(5) of e^{2x} is 8

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

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

8

Solution steps

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

Apply u-substitution

: \int_{2 l n (3)}^{2 l n (5)} e^{u} \frac{1}{2} d u

= \int_{2 l n (3)}^{2 l n (5)} e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{2 l n (3)}^{2 l n (5)} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{2 l n (3)}^{2 l n (5)}

Compute the boundaries:

16

= \frac{1}{2} \cdot 16

Simplify

= 8

f (x) = 3^{x}, at x = 0

\int - 9 sin (3 t) d t

x \to 1 lim (x^{17} - x + 3)

\frac{d}{d x} (3 x^{2} + 2 y^{4})

What is the integral from ln(3) to ln(5) of e^{2x} ?
The integral from ln(3) to ln(5) of e^{2x} is 8