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

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

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integral of sqrt(5x-3)

\int 5 x - 3 d x

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

Solution steps

\int 5 x - 3 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 - 3

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

Simplify

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

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

Add a constant to the solution

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

x \to 0 lim (e^{π (x + 1)})

y^{^{'}} = 2 x y^{2} + 3 x^{2} y^{2}

x \to - 7 lim (\frac{1}{x ^{2} ( x + 7 )})

x^{^{''}} + x = e^{2 t}

\frac{\partial}{\partial x} (ln (x + 8 y + 4 z))

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