What is the integral from 0 to 3 of sqrt(4x+5) ?

The integral from 0 to 3 of sqrt(4x+5) is (17sqrt(17)-5sqrt(5))/6

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integral from 0 to 3 of sqrt(4x+5)

\int_{0}^{3} 4 x + 5 d x

\frac{17 17 - 5 5}{6}

Decimal

9.81874 \dots

Solution steps

\int_{0}^{3} 4 x + 5 d x

Apply u-substitution

: \int_{5}^{17} \frac{u}{4} d u

= \int_{5}^{17} \frac{u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{5}^{17} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{17}

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{17}

Compute the boundaries:

\frac{34 17 - 10 5}{3}

= \frac{1}{4} \cdot \frac{34 17 - 10 5}{3}

Simplify

= \frac{17 17 - 5 5}{6}

x = - 3, x = - 1, y = x^{3} + 8, y = 0

\frac{\partial}{\partial x} (y^{2} e^{- x})

\frac{\partial}{\partial x} ((A x^{c} + B y^{c})^{\frac{1}{c}})

\frac{\partial}{\partial x} (\frac{18}{x y})

\int_{1}^{6} k x d x

What is the integral from 0 to 3 of sqrt(4x+5) ?
The integral from 0 to 3 of sqrt(4x+5) is (17sqrt(17)-5sqrt(5))/6