What is the integral of sqrt(1+3x) ?

The integral of sqrt(1+3x) is 2/9 (1+3x)^{3/2}+C

Popular >

integral of sqrt(1+3x)

\int 1 + 3 x d x

\frac{2}{9} (1 + 3 x)^{\frac{3}{2}} + C

Solution steps

\int 1 + 3 x d x

Apply u-substitution

: \int \frac{u}{3} d u

= \int \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = 1 + 3 x

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

Simplify

\frac{1}{3} \cdot \frac{2}{3} (1 + 3 x)^{\frac{3}{2}} : \frac{2}{9} (1 + 3 x)^{\frac{3}{2}}

= \frac{2}{9} (1 + 3 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (1 + 3 x)^{\frac{3}{2}} + C

y = cos (x^{2}) 2 x

n = 1 \sum \infty \frac{( e ^{\frac{8}{n}} )}{n}

\frac{d}{d x} ((\frac{x - 7}{x - 9})^{4})

\int \frac{ln ( 20 x )}{x} d x

\frac{d}{d y} (- e^{y})

What is the integral of sqrt(1+3x) ?
The integral of sqrt(1+3x) is 2/9 (1+3x)^{3/2}+C