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

The integral from 0 to ln(3) of e^{4x} is 20

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

\int_{0}^{l n (3)} e^{4 x} d x

20

Solution steps

\int_{0}^{l n (3)} e^{4 x} d x

Apply u-substitution

: \int_{0}^{4 l n (3)} e^{u} \frac{1}{4} d u

= \int_{0}^{4 l n (3)} e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{4 l n (3)} e^{u} d u

Use the common integral:

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

= \frac{1}{4} [e^{u}]_{0}^{4 l n (3)}

Compute the boundaries:

80

= \frac{1}{4} \cdot 80

Simplify

= 20

\int (4 x y) d x

\int 5 x cos (5 x) d x

f (x) = x^{2} - 5 x + 3

\int 4 sin (y) d y

\frac{d}{d x} (e^{- 4 x} sin (3 x))

What is the integral from 0 to ln(3) of e^{4x} ?
The integral from 0 to ln(3) of e^{4x} is 20