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

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

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integral of sqrt(5-2x)

\int 5 - 2 x d x

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

Solution steps

\int 5 - 2 x 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 = 5 - 2 x

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

Simplify

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

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

Add a constant to the solution

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

t \to 0 lim (cos (t))

\int - cos (x) + sin (x) + 1 d x

n = 2 \sum \infty 5 (- \frac{1}{3})^{n}

\int \frac{5 x ^{2}}{2} d x

y = \frac{3 ln ( 4 x )}{5 - 2 x}

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