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

The integral of 1/(sqrt(5x+4)) is 2/5 sqrt(5x+4)+C

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

\int \frac{1}{5 x + 4} d x

\frac{2}{5} 5 x + 4 + C

Solution steps

\int \frac{1}{5 x + 4} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= \frac{1}{5} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 5 x + 4

= \frac{1}{5} \cdot 2 (5 x + 4)^{\frac{1}{2}}

Simplify

\frac{1}{5} \cdot 2 (5 x + 4)^{\frac{1}{2}} : \frac{2}{5} 5 x + 4

= \frac{2}{5} 5 x + 4

Add a constant to the solution

= \frac{2}{5} 5 x + 4 + C

n = 1 \sum \infty \frac{8 n}{7 - 4 n}

\frac{d}{d x} (3 tan (2^{- x}))

x (1 + y^{2}) d x + y (1 + x^{2}) d y = 0

x \to 0 lim (x (1))

\frac{d}{d x} (- \frac{cos ( 3 x )}{3})

What is the integral of 1/(sqrt(5x+4)) ?
The integral of 1/(sqrt(5x+4)) is 2/5 sqrt(5x+4)+C