What is the integral of x/(sqrt(6x^2+1)) ?

The integral of x/(sqrt(6x^2+1)) is 1/6 sqrt(6x^2+1)+C

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integral of x/(sqrt(6x^2+1))

\int \frac{x}{6 x ^{2} + 1} d x

\frac{1}{6} 6 x^{2} + 1 + C

Solution steps

\int \frac{x}{6 x ^{2} + 1} d x

Apply u-substitution

: \int \frac{1}{12 u} d u

= \int \frac{1}{12 u} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= \frac{1}{12} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 6 x^{2} + 1

= \frac{1}{12} \cdot 2 (6 x^{2} + 1)^{\frac{1}{2}}

Simplify

\frac{1}{12} \cdot 2 (6 x^{2} + 1)^{\frac{1}{2}} : \frac{1}{6} 6 x^{2} + 1

= \frac{1}{6} 6 x^{2} + 1

Add a constant to the solution

= \frac{1}{6} 6 x^{2} + 1 + C

(2 x + 2 y)^{3} = 8 x^{3} + 8 y^{3}

\int (\frac{tan ( x )}{sin ( x ) cos ( x )}) d x

f (x) \frac{3}{x}

f (x) = 2 x^{2} + 3, x, [- 1, 2]

x \to - 2 lim (x^{2} + x - 2)

What is the integral of x/(sqrt(6x^2+1)) ?
The integral of x/(sqrt(6x^2+1)) is 1/6 sqrt(6x^2+1)+C