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

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

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

integral

\frac{2}{2 x + 1}

2 2 x + 1 + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int \frac{1}{2 x + 1} d x

Apply u-substitution

: \int 1 d u

= 2 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot 1 \cdot u

Substitute back

u = 2 x + 1

= 2 \cdot 1 \cdot 2 x + 1

Simplify

= 2 2 x + 1

Add a constant to the solution

= 2 2 x + 1 + C

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

ln (\frac{x}{( 10 - x )})

\frac{( x - 3 )}{( x ^{2} - 3 x + 2 )}

\frac{x ^{3}}{x ^{4} + 1}

e^{3 x - 1}

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