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

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

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

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

ln 1 + x + C

Solution steps

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

Apply u-substitution

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

Apply u-substitution

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln 1 + x

Add a constant to the solution

= ln 1 + x + C

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