What is the integral from ln(8) to ln(27) of e^{x/3} ?

The integral from ln(8) to ln(27) of e^{x/3} is 3

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integral from ln(8) to ln(27) of e^{x/3}

\int_{l n (8)}^{l n (27)} e^{\frac{x}{3}} d x

3

Solution steps

\int_{l n (8)}^{l n (27)} e^{\frac{x}{3}} d x

Apply u-substitution

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

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

Use the common integral:

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

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

Compute the boundaries:

1

= 3 \cdot 1

Simplify

= 3

\frac{d}{d x} (sech^{2} (x))

- 72 e^{- 2 x}

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

5 cos (3 t)

What is the integral from ln(8) to ln(27) of e^{x/3} ?
The integral from ln(8) to ln(27) of e^{x/3} is 3