What is the integral of sqrt(1+x/4) ?

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

Popular >

integral of sqrt(1+x/4)

\int 1 + \frac{x}{4} d x

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

Solution steps

\int 1 + \frac{x}{4} d x

Apply u-substitution

: \int u \cdot 4 d u

= \int u \cdot 4 d u

Take the constant out:

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

= 4 \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = 1 + \frac{x}{4}

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

Simplify

4 \cdot \frac{2}{3} (1 + \frac{x}{4})^{\frac{3}{2}} : \frac{1}{3} (4 + x)^{\frac{3}{2}}

= \frac{1}{3} (4 + x)^{\frac{3}{2}}

Add a constant to the solution

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

\int \frac{( x ^{2} - 1 )}{2 x - 1} d x

x \to 0 lim (\frac{0}{x ^{2} ∣ x ∣})

\frac{d y}{d t} = t^{2} + 20 t^{2} y

\int \frac{1}{9 z ^{2} - 25} d z

y = 2 t (3 t^{2} - 5)^{4}

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