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

The integral from 2 to 5 of e^{2x} is (e^{10}-e^4)/2

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

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

\frac{e ^{10} - e ^{4}}{2}

Decimal

10985.93382 \dots

Solution steps

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

Apply u-substitution

: \int_{4}^{10} e^{u} \frac{1}{2} d u

= \int_{4}^{10} e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{4}^{10} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{4}^{10}

Compute the boundaries:

e^{10} - e^{4}

= \frac{1}{2} (e^{10} - e^{4})

Simplify

= \frac{e ^{10} - e ^{4}}{2}

\frac{\partial}{\partial x} (4 x^{5} - 2 y^{- 3})

\frac{9 + 2 x - 6 x}{x}

y^{^{''}} + y^{^{'}} - 2 y = 0

\frac{d}{d x} (- x^{4} + 50 x^{2} - 300)

(4.1) (7.1)

What is the integral from 2 to 5 of e^{2x} ?
The integral from 2 to 5 of e^{2x} is (e^{10}-e^4)/2