Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Rewrite the fraction $\frac{\ln\left(x\right)}{x\sqrt{1+\ln\left(x\right)}}$ inside the integral as the product of two functions: $\frac{1}{x\sqrt{1+\ln\left(x\right)}}\ln\left(x\right)$
Learn how to solve integrals involving logarithmic functions problems step by step online.
$\int\frac{1}{x\sqrt{1+\ln\left(x\right)}}\ln\left(x\right)dx$
Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(ln(x)/(x(1+ln(x))^1/2))dx. Rewrite the fraction \frac{\ln\left(x\right)}{x\sqrt{1+\ln\left(x\right)}} inside the integral as the product of two functions: \frac{1}{x\sqrt{1+\ln\left(x\right)}}\ln\left(x\right). We can solve the integral \int\frac{1}{x\sqrt{1+\ln\left(x\right)}}\ln\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.