What is the integral from 0 to ln(2) of e^{5x} ?

The integral from 0 to ln(2) of e^{5x} is 31/5

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integral from 0 to ln(2) of e^{5x}

\int_{0}^{l n (2)} e^{5 x} d x

\frac{31}{5}

Decimal

6.2

Solution steps

\int_{0}^{l n (2)} e^{5 x} d x

Apply u-substitution

: \int_{0}^{5 l n (2)} e^{u} \frac{1}{5} d u

= \int_{0}^{5 l n (2)} e^{u} \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{0}^{5 l n (2)} e^{u} d u

Use the common integral:

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

= \frac{1}{5} [e^{u}]_{0}^{5 l n (2)}

Compute the boundaries:

31

= \frac{1}{5} \cdot 31

Simplify

= \frac{31}{5}

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What is the integral from 0 to ln(2) of e^{5x} ?
The integral from 0 to ln(2) of e^{5x} is 31/5