What is the integral from 1 to 5 of 1/(sqrt(4x+5)) ?

The integral from 1 to 5 of 1/(sqrt(4x+5)) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 5 of 1/(sqrt(4x+5))

\int_{1}^{5} \frac{1}{4 x + 5} d x

1

Solution steps

\int_{1}^{5} \frac{1}{4 x + 5} d x

Apply u-substitution

: \int_{9}^{25} \frac{1}{4 u} d u

= \int_{9}^{25} \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_{9}^{25} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{9}^{25}

= \frac{1}{4} [2 u^{\frac{1}{2}}]_{9}^{25}

Apply radical rule:

a^{\frac{1}{n}} = n a

= \frac{1}{4} [2 u]_{9}^{25}

Compute the boundaries:

4

= \frac{1}{4} \cdot 4

Simplify

= 1

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

x \to - 4 lim (5 x + 1)

\frac{d}{d x} (arctan (x^{2} - 1))

- \frac{6 x}{y}

t \to 0 lim (\frac{t}{tan ( 3 t )})

What is the integral from 1 to 5 of 1/(sqrt(4x+5)) ?
The integral from 1 to 5 of 1/(sqrt(4x+5)) is 1