What is the integral from 1 to 3 of 2e^{5x} ?

The integral from 1 to 3 of 2e^{5x} is (2(e^{15}-e^5))/5

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integral from 1 to 3 of 2e^{5x}

\int_{1}^{3} 2 e^{5 x} d x

\frac{2 ( e ^{15} - e ^{5} )}{5}

Decimal Notation

1307547.58372 \dots

Solution steps

\int_{1}^{3} 2 e^{5 x} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{3} e^{5 x} d x

Apply u-substitution

: \int_{5}^{15} e^{u} \frac{1}{5} d u

= 2 \cdot \int_{5}^{15} 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

= 2 \cdot \frac{1}{5} \cdot \int_{5}^{15} e^{u} d u

Use the common integral:

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

= 2 \cdot \frac{1}{5} [e^{u}]_{5}^{15}

Simplify

2 \cdot \frac{1}{5} [e^{u}]_{5}^{15} : \frac{2}{5} [e^{u}]_{5}^{15}

= \frac{2}{5} [e^{u}]_{5}^{15}

Compute the boundaries:

e^{15} - e^{5}

= \frac{2}{5} (e^{15} - e^{5})

Simplify

= \frac{2 ( e ^{15} - e ^{5} )}{5}

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What is the integral from 1 to 3 of 2e^{5x} ?
The integral from 1 to 3 of 2e^{5x} is (2(e^{15}-e^5))/5