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

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

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

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

1 + 2 x + C

Solution steps

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

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = 1 + 2 x

= 1 \cdot 1 + 2 x

Simplify

= 1 + 2 x

Add a constant to the solution

= 1 + 2 x + C

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