What is the integral of 1/(xsqrt(5+ln(3x))) ?

The integral of 1/(xsqrt(5+ln(3x))) is 2sqrt(5+ln(3x))+C

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integral of 1/(xsqrt(5+ln(3x)))

\int \frac{1}{x 5 + ln ( 3 x )} d x

2 5 + ln (3 x) + C

Solution steps

\int \frac{1}{x 5 + ln ( 3 x )} d x

Apply u-substitution

: \int \frac{1}{u 5 + ln ( u )} d u

= \int \frac{1}{u 5 + ln ( u )} d u

Apply u-substitution

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

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

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= 2 v^{\frac{1}{2}}

Substitute back

= 2 (5 + ln (3 x))^{\frac{1}{2}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 5 + ln (3 x)

Add a constant to the solution

= 2 5 + ln (3 x) + C

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What is the integral of 1/(xsqrt(5+ln(3x))) ?
The integral of 1/(xsqrt(5+ln(3x))) is 2sqrt(5+ln(3x))+C