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

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

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integral of 1/(xsqrt(1+2ln(x)))

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

1 + 2 ln (x) + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{1 + 2 u} d u

Apply u-substitution

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

= 1 \cdot 1 + 2 ln (x)

Simplify

= 1 + 2 ln (x)

Add a constant to the solution

= 1 + 2 ln (x) + C

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