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

The integral of sqrt(5x-1) is 2/15 (5x-1)^{3/2}+C

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integral of sqrt(5x-1)

\int 5 x - 1 d x

\frac{2}{15} (5 x - 1)^{\frac{3}{2}} + C

Solution steps

\int 5 x - 1 d x

Apply u-substitution

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

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

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{1}{5} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 5 x - 1

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

Simplify

\frac{1}{5} \cdot \frac{2}{3} (5 x - 1)^{\frac{3}{2}} : \frac{2}{15} (5 x - 1)^{\frac{3}{2}}

= \frac{2}{15} (5 x - 1)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{15} (5 x - 1)^{\frac{3}{2}} + C

\frac{d y}{d x} = 8 - \frac{y}{50}, y (0) = 50

y^{^{''}} = 6 t

f (x) = \frac{1}{x ^{8}}

\frac{d}{d x} (x + \frac{1}{x})

\int 2 x + 5 d x

What is the integral of sqrt(5x-1) ?
The integral of sqrt(5x-1) is 2/15 (5x-1)^{3/2}+C