What is the integral from 1 to 4 of 1/(sqrt(4x+7)) ?

The integral from 1 to 4 of 1/(sqrt(4x+7)) is (sqrt(23)-sqrt(11))/2

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integral from 1 to 4 of 1/(sqrt(4x+7))

\int_{1}^{4} \frac{1}{4 x + 7} d x

\frac{23 - 11}{2}

Decimal Notation

0.73960 \dots

Solution steps

\int_{1}^{4} \frac{1}{4 x + 7} d x

Apply u-substitution

: \int_{11}^{23} \frac{1}{4 u} d u

= \int_{11}^{23} \frac{1}{4 u} 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_{11}^{23} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{11}^{23}

= \frac{1}{4} [2 u^{\frac{1}{2}}]_{11}^{23}

Apply radical rule:

= \frac{1}{4} [2 u]_{11}^{23}

Compute the boundaries:

223 - 211

= \frac{1}{4} (223 - 211)

Simplify

= \frac{23 - 11}{2}

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What is the integral from 1 to 4 of 1/(sqrt(4x+7)) ?
The integral from 1 to 4 of 1/(sqrt(4x+7)) is (sqrt(23)-sqrt(11))/2