What is the integral from 1 to 4 of e^{3sqrt(x)} ?

The integral from 1 to 4 of e^{3sqrt(x)} is (2(5e^6-2e^3))/9

Popular >

integral from 1 to 4 of e^{3sqrt(x)}

\int_{1}^{4} e^{3 x} d x

\frac{2 ( 5 e ^{6} - 2 e ^{3} )}{9}

Decimal

439.32730 \dots

Solution steps

\int_{1}^{4} e^{3 x} d x

Apply u-substitution

: \int_{3}^{6} \frac{2 e ^{u} u}{9} d u

= \int_{3}^{6} \frac{2 e ^{u} u}{9} d u

Take the constant out:

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

= \frac{2}{9} \cdot \int_{3}^{6} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{3}^{6}

= \frac{2}{9} [e^{u} u - \int e^{u} d u]_{3}^{6}

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

= \frac{2}{9} [e^{u} u - e^{u}]_{3}^{6}

Compute the boundaries:

5 e^{6} - 2 e^{3}

= \frac{2}{9} (5 e^{6} - 2 e^{3})

Simplify

= \frac{2 ( 5 e ^{6} - 2 e ^{3} )}{9}

\int_{0}^{s i n (x)} e^{- t^{2}} d t

\int_{- 1}^{8} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{0}^{1} 2 sin (x) d x

\int_{0}^{l n (3)} e^{6 x} d x

\int_{2}^{7} 3 v d v

What is the integral from 1 to 4 of e^{3sqrt(x)} ?
The integral from 1 to 4 of e^{3sqrt(x)} is (2(5e^6-2e^3))/9