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

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

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integral of sqrt(2x-1)

\int 2 x - 1 d x

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

Solution steps

\int 2 x - 1 d x

Apply u-substitution

: \int \frac{u}{2} d u

= \int \frac{u}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = 2 x - 1

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

Simplify

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

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

Add a constant to the solution

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

\int 16 θ sec^{2} (θ) d θ

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 4, y^{^{'}} (0) = 0

\int_{- \frac{1}{3}}^{0} \frac{3}{4} (1 - x^{2}) d x

x + x^{2} + ln (x)

x \to + 2 π lim (f (x))

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