What is the integral from 0 to 1 of 5/(sqrt(7x+9)) ?

The integral from 0 to 1 of 5/(sqrt(7x+9)) is 10/7

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integral from 0 to 1 of 5/(sqrt(7x+9))

\int_{0}^{1} \frac{5}{7 x + 9} d x

\frac{10}{7}

Decimal

1.42857 \dots

Solution steps

\int_{0}^{1} \frac{5}{7 x + 9} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{1} \frac{1}{7 x + 9} d x

Apply u-substitution

: \int_{9}^{16} \frac{1}{7 u} d u

= 5 \cdot \int_{9}^{16} \frac{1}{7 u} d u

Take the constant out:

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

= 5 \cdot \frac{1}{7} \cdot \int_{9}^{16} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{9}^{16}

= 5 \cdot \frac{1}{7} [2 u^{\frac{1}{2}}]_{9}^{16}

Simplify

5 \cdot \frac{1}{7} [2 u^{\frac{1}{2}}]_{9}^{16} : \frac{5}{7} [2 u]_{9}^{16}

= \frac{5}{7} [2 u]_{9}^{16}

Compute the boundaries:

2

= \frac{5}{7} \cdot 2

Simplify

= \frac{10}{7}

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What is the integral from 0 to 1 of 5/(sqrt(7x+9)) ?
The integral from 0 to 1 of 5/(sqrt(7x+9)) is 10/7