What is the integral of 1/(sqrt(5x-3)) ?

The integral of 1/(sqrt(5x-3)) is 2/5 sqrt(5x-3)+C

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integral of 1/(sqrt(5x-3))

\int \frac{1}{5 x - 3} d x

\frac{2}{5} 5 x - 3 + C

Solution steps

\int \frac{1}{5 x - 3} 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 - 3

= \frac{1}{5} \cdot 2 (5 x - 3)^{\frac{1}{2}}

Simplify

\frac{1}{5} \cdot 2 (5 x - 3)^{\frac{1}{2}} : \frac{2}{5} 5 x - 3

= \frac{2}{5} 5 x - 3

Add a constant to the solution

= \frac{2}{5} 5 x - 3 + C

h \to 0 lim (\frac{( 2 ^{h} - 1 )}{h})

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

\frac{d}{d x} (π x^{2})

\int \frac{x ^{2} + 24 x ^{3}}{x} d x

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

What is the integral of 1/(sqrt(5x-3)) ?
The integral of 1/(sqrt(5x-3)) is 2/5 sqrt(5x-3)+C