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

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

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integral of 1/(sqrt(x)(1+2\sqrt{x))}

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

ln 1 + 2 x + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + 2 x

= ln 1 + 2 x

Add a constant to the solution

= ln 1 + 2 x + C

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