What is the integral from 0 to ln(3) of e^{5x} ?

The integral from 0 to ln(3) of e^{5x} is 242/5

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integral from 0 to ln(3) of e^{5x}

\int_{0}^{l n (3)} e^{5 x} d x

\frac{242}{5}

Decimal

48.4

Solution steps

\int_{0}^{l n (3)} e^{5 x} d x

Apply u-substitution

: \int_{0}^{5 l n (3)} e^{u} \frac{1}{5} d u

= \int_{0}^{5 l n (3)} 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 (3)} e^{u} d u

Use the common integral:

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

= \frac{1}{5} [e^{u}]_{0}^{5 l n (3)}

Compute the boundaries:

242

= \frac{1}{5} \cdot 242

Simplify

= \frac{242}{5}

\int_{0}^{3} ∣ 3 x - 2 ∣ d x

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\int_{- 2}^{3} (2 x^{4} + 5 x^{3} - x + 5) d x

\int_{- 2}^{0} x 2 x^{2} + 1 d x

\int_{0}^{1} (1 + \frac{9}{4} x)^{\frac{1}{2}} d x

What is the integral from 0 to ln(3) of e^{5x} ?
The integral from 0 to ln(3) of e^{5x} is 242/5