What is the integral of 1/(sqrt(5x-2)) ?

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

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integral of 1/(sqrt(5x-2))

\int \frac{1}{5 x - 2} d x

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

Solution steps

\int \frac{1}{5 x - 2} 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 - 2

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{1}{( 1 + u ) ^{2}} d u

\frac{d r}{d θ} = 8 (cos (\frac{θ}{3}))^{3}

x \to 0 + lim ((e^{x} + x)^{\frac{2}{x}})

y^{^{''}} + 10 y^{^{'}} + 2500 = 500 sin (100 x)

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

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