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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: $\frac{1}{x\sqrt{1+\ln\left(x\right)}}\ln\left(x\right)$
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$\int\frac{1}{x\sqrt{1+\ln\left(x\right)}}\ln\left(x\right)dx$
Learn how to solve differential equations 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 u and calculate du. Now, identify dv and calculate v.