What is the integral from 0 to ln(3) of e^{2x} ?

The integral from 0 to ln(3) of e^{2x} is 4

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integral from 0 to ln(3) of e^{2x}

\int_{0}^{l n (3)} e^{2 x} d x

4

Solution steps

\int_{0}^{l n (3)} e^{2 x} d x

Apply u-substitution

: \int_{0}^{2 l n (3)} e^{u} \frac{1}{2} d u

= \int_{0}^{2 l n (3)} 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_{0}^{2 l n (3)} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{0}^{2 l n (3)}

Compute the boundaries:

8

= \frac{1}{2} \cdot 8

Simplify

= 4

x \to 0 + lim (3 x^{\frac{x}{2}})

y = 3 x, y = 9 x^{2}

y^{^{''}} + 4 y = 9 e^{2 t} sin (2 t) + 5 t^{2}

sec (x)

x \to 0 lim (arctan (x))

What is the integral from 0 to ln(3) of e^{2x} ?
The integral from 0 to ln(3) of e^{2x} is 4