What is the integral from 0 to ln(6) of e^{5x} ?

The integral from 0 to ln(6) of e^{5x} is 1555

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integral from 0 to ln(6) of e^{5x}

\int_{0}^{l n (6)} e^{5 x} d x

1555

Solution steps

\int_{0}^{l n (6)} e^{5 x} d x

Apply u-substitution

= \int_{0}^{5 l n (6)} 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 (6)} e^{u} d u

Use the common integral:

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

= \frac{1}{5} [e^{u}]_{0}^{5 l n (6)}

Compute the boundaries:

7775

= \frac{1}{5} \cdot 7775

Simplify

= 1555

What is the integral from 0 to ln(6) of e^{5x} ?
The integral from 0 to ln(6) of e^{5x} is 1555