What is the integral of sqrt(1+8x) ?

The integral of sqrt(1+8x) is 1/12 (1+8x)^{3/2}+C

Popular >

integral of sqrt(1+8x)

\int 1 + 8 x d x

\frac{1}{12} (1 + 8 x)^{\frac{3}{2}} + C

Solution steps

\int 1 + 8 x d x

Apply u-substitution

: \int \frac{u}{8} d u

= \int \frac{u}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{8} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 + 8 x

= \frac{1}{8} \cdot \frac{2}{3} (1 + 8 x)^{\frac{3}{2}}

Simplify

\frac{1}{8} \cdot \frac{2}{3} (1 + 8 x)^{\frac{3}{2}} : \frac{1}{12} (1 + 8 x)^{\frac{3}{2}}

= \frac{1}{12} (1 + 8 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{12} (1 + 8 x)^{\frac{3}{2}} + C

\int a r tan (x) d x

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

\int 2 cos^{3} (2 x) d x

sin (θ) + csc (θ)

\frac{d}{d x} (\frac{a ^{2} + x ^{2}}{a ^{2} - x ^{2}})

What is the integral of sqrt(1+8x) ?
The integral of sqrt(1+8x) is 1/12 (1+8x)^{3/2}+C