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

The integral from 0 to ln(2) of e^{4x} is 15/4

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

\int_{0}^{l n (2)} e^{4 x} d x

\frac{15}{4}

Decimal

3.75

Solution steps

\int_{0}^{l n (2)} e^{4 x} d x

Apply u-substitution

= \int_{0}^{4 l n (2)} 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 (2)} e^{u} d u

Use the common integral:

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

= \frac{1}{4} [e^{u}]_{0}^{4 l n (2)}

Compute the boundaries:

15

= \frac{1}{4} \cdot 15

Simplify

= \frac{15}{4}

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What is the integral from 0 to ln(2) of e^{4x} ?
The integral from 0 to ln(2) of e^{4x} is 15/4