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

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

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integral of sqrt(2x-5)

\int 2 x - 5 d x

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

Solution steps

\int 2 x - 5 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 - 5

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

Simplify

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

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

Add a constant to the solution

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

x \to 2 lim ((3 - x)^{2})

\int (3 x^{2} - 7 x)^{5} (6 x - 7) d x

\int x (e^{(3 x - 2)} + 5) d x

tan (θ)

x \to 9 + lim (\frac{∣ x - 9 ∣}{x - 9})

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