What is the integral of sqrt(5-4x) ?

The integral of sqrt(5-4x) is -1/6 (5-4x)^{3/2}+C

integral of sqrt(5-4x)

\int 5 - 4 x d x

- \frac{1}{6} (5 - 4 x)^{\frac{3}{2}} + C

Solution steps

\int 5 - 4 x d x

Apply u-substitution

= \int - \frac{u}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int u d u

Apply the Power Rule

= - \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 5 - 4 x

= - \frac{1}{4} \cdot \frac{2}{3} (5 - 4 x)^{\frac{3}{2}}

Simplify

- \frac{1}{4} \cdot \frac{2}{3} (5 - 4 x)^{\frac{3}{2}} : - \frac{1}{6} (5 - 4 x)^{\frac{3}{2}}

= - \frac{1}{6} (5 - 4 x)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{1}{6} (5 - 4 x)^{\frac{3}{2}} + C

\int_{0}^{1} \frac{1}{1 + x ^{2}} d x

\int e^{1 - 3 x} d x

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

x \to 9 + lim (\frac{1}{x - 9})

t an g e n t y = x^{4}, (- 1, 1)

What is the integral of sqrt(5-4x) ?
The integral of sqrt(5-4x) is -1/6 (5-4x)^{3/2}+C