What is the integral from 0 to ln(6) of e^{2x} ?

The integral from 0 to ln(6) of e^{2x} is 35/2

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integral from 0 to ln(6) of e^{2x}

\int_{0}^{l n (6)} e^{2 x} d x

\frac{35}{2}

Decimal

17.5

Solution steps

\int_{0}^{l n (6)} e^{2 x} d x

Apply u-substitution

: \int_{0}^{2 l n (6)} e^{u} \frac{1}{2} d u

= \int_{0}^{2 l n (6)} 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 (6)} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{0}^{2 l n (6)}

Compute the boundaries:

35

= \frac{1}{2} \cdot 35

Simplify

= \frac{35}{2}

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What is the integral from 0 to ln(6) of e^{2x} ?
The integral from 0 to ln(6) of e^{2x} is 35/2