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

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

Popular >

integral of sqrt(4x+5)

\int 4 x + 5 d x

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

Solution steps

\int 4 x + 5 d x

Apply u-substitution

: \int \frac{u}{4} d u

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

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

Substitute back

u = 4 x + 5

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

Simplify

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

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

Add a constant to the solution

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

x \to 1 lim (\frac{tan ( x )}{x})

\int 100 e^{- 0.01 x} d x

x \to 0 lim (e^{\frac{1}{x}})

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

f (x) = 8 x + ln (x^{2}), at x = 1

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