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

The integral of 1/(sqrt(3x+1)) is 2/3 sqrt(3x+1)+C

Popular >

integral of 1/(sqrt(3x+1))

\int \frac{1}{3 x + 1} d x

\frac{2}{3} 3 x + 1 + C

Solution steps

\int \frac{1}{3 x + 1} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

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

Apply the Power Rule

: 2 u^{\frac{1}{2}}

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

Substitute back

u = 3 x + 1

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

Simplify

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

= \frac{2}{3} 3 x + 1

Add a constant to the solution

= \frac{2}{3} 3 x + 1 + C

\int 64 d x

\int x^{2} (x^{3} + 8)^{2} d x

n = 1 \sum \infty 2 (0.5)^{n - 1}

\frac{\partial}{\partial x} (ln (\frac{1}{x ^{2} + y ^{2}}))

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

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