What is the integral from ln(8) to ln(64) of e^{x/3} ?

The integral from ln(8) to ln(64) of e^{x/3} is 6

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integral from ln(8) to ln(64) of e^{x/3}

\int_{l n (8)}^{l n (64)} e^{\frac{x}{3}} d x

6

Solution steps

\int_{l n (8)}^{l n (64)} e^{\frac{x}{3}} d x

Apply u-substitution

= \int_{l n (2)}^{2 l n (2)} e^{u} \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int_{l n (2)}^{2 l n (2)} e^{u} d u

Use the common integral:

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

= 3 [e^{u}]_{l n (2)}^{2 l n (2)}

Compute the boundaries:

2

= 3 \cdot 2

Simplify

= 6

What is the integral from ln(8) to ln(64) of e^{x/3} ?
The integral from ln(8) to ln(64) of e^{x/3} is 6