What is the integral from 2 to 4 of 3e^{3x} ?

The integral from 2 to 4 of 3e^{3x} is e^{12}-e^6

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integral from 2 to 4 of 3e^{3x}

\int_{2}^{4} 3 e^{3 x} d x

e^{12} - e^{6}

Decimal

162351.36262 \dots

Solution steps

\int_{2}^{4} 3 e^{3 x} d x

Take the constant out:

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

= 3 \cdot \int_{2}^{4} e^{3 x} d x

Apply u-substitution

: \int_{6}^{12} e^{u} \frac{1}{3} d u

= 3 \cdot \int_{6}^{12} e^{u} \frac{1}{3} d u

Take the constant out:

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

= 3 \cdot \frac{1}{3} \cdot \int_{6}^{12} e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{3} [e^{u}]_{6}^{12}

Simplify

3 \cdot \frac{1}{3} [e^{u}]_{6}^{12} : [e^{u}]_{6}^{12}

= [e^{u}]_{6}^{12}

Compute the boundaries:

e^{12} - e^{6}

= e^{12} - e^{6}

\frac{d}{d x} (6 e^{x})

x \to 1 lim (3 x + 1)

\int x (ln (x))^{3} d x

\int \frac{e ^{3 x}}{1 + e ^{x}} d x

x \to 3 lim (x^{2} + 3 x - 1)

What is the integral from 2 to 4 of 3e^{3x} ?
The integral from 2 to 4 of 3e^{3x} is e^{12}-e^6