What is the integral of 1/(sqrt(x)(1-3\sqrt{x))} ?

The integral of 1/(sqrt(x)(1-3\sqrt{x))} is -2/3 ln|1-3sqrt(x)|+C

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integral of 1/(sqrt(x)(1-3\sqrt{x))}

\int \frac{1}{x ( 1 - 3 x )} d x

- \frac{2}{3} ln 1 - 3 x + C

Solution steps

\int \frac{1}{x ( 1 - 3 x )} d x

Apply u-substitution

: \int - \frac{2}{3 u} d u

= \int - \frac{2}{3 u} d u

Take the constant out:

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

= - \frac{2}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{2}{3} ln ∣ u ∣

Substitute back

u = 1 - 3 x

= - \frac{2}{3} ln 1 - 3 x

Add a constant to the solution

= - \frac{2}{3} ln 1 - 3 x + C

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What is the integral of 1/(sqrt(x)(1-3\sqrt{x))} ?
The integral of 1/(sqrt(x)(1-3\sqrt{x))} is -2/3 ln|1-3sqrt(x)|+C