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

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

Popular >

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

y = ln (x x^{2} - 1)

\frac{d y}{d x} = 2 y - 4

\frac{d}{d x} (8 x^{3} - 8)

5 cot (x)

x \to - 2 lim (3 x^{4})

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