What is the integral of sqrt(7-2x) ?

The integral of sqrt(7-2x) is -1/3 (7-2x)^{3/2}+C

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integral of sqrt(7-2x)

\int 7 - 2 x d x

- \frac{1}{3} (7 - 2 x)^{\frac{3}{2}} + C

Solution steps

\int 7 - 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 = 7 - 2 x

= - \frac{1}{2} \cdot \frac{2}{3} (7 - 2 x)^{\frac{3}{2}}

Simplify

- \frac{1}{2} \cdot \frac{2}{3} (7 - 2 x)^{\frac{3}{2}} : - \frac{1}{3} (7 - 2 x)^{\frac{3}{2}}

= - \frac{1}{3} (7 - 2 x)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{1}{3} (7 - 2 x)^{\frac{3}{2}} + C

\frac{d}{d x} (\frac{3 x ^{2} tan ( x )}{sec ( x )})

sin (cos (tan (π x)))

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

x \to 2 + lim (\frac{x}{x ^{2} + 4})

x \to 7 lim (\frac{6 x}{x - 7})

What is the integral of sqrt(7-2x) ?
The integral of sqrt(7-2x) is -1/3 (7-2x)^{3/2}+C