What is the integral of s/(sqrt(3s^2+1)) ?

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

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integral of s/(sqrt(3s^2+1))

\int \frac{s}{3 s ^{2} + 1} d s

\frac{1}{3} 3 s^{2} + 1 + C

Solution steps

\int \frac{s}{3 s ^{2} + 1} d s

Apply u-substitution

: \int \frac{1}{6 u} d u

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= \frac{1}{6} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 3 s^{2} + 1

= \frac{1}{6} \cdot 2 (3 s^{2} + 1)^{\frac{1}{2}}

Simplify

\frac{1}{6} \cdot 2 (3 s^{2} + 1)^{\frac{1}{2}} : \frac{1}{3} 3 s^{2} + 1

= \frac{1}{3} 3 s^{2} + 1

Add a constant to the solution

= \frac{1}{3} 3 s^{2} + 1 + C

\frac{d}{d x} (\frac{e ^{2 x + 1}}{2 x + 5})

n = 1 \sum \infty \frac{ln ( n )}{2 n}

y = \frac{3}{x}, y = 12 x

\frac{\partial}{\partial x} (y^{\frac{z}{x}})

\int \frac{( 8 x - 3 )}{( 4 x ^{2} + ( - 3 ) x )} d x

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