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

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

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

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

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

Solution steps

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

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 s + 4

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

Simplify

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

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

Add a constant to the solution

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

x \to + 3 lim (3 x^{2} + 4 x - 1)

x \to 6 lim (4 x)

x + x

7 u + 10 u

x + 3

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