Exercise
$\int\frac{\left(1+logx\right)}{x}dx$
Step-by-step Solution
Learn how to solve differential calculus problems step by step online. Solve the integral of logarithmic functions int((1+log(x))/x)dx. Expand the fraction \frac{1+\log \left(x\right)}{x} into 2 simpler fractions with common denominator x. Expand the integral \int\left(\frac{1}{x}+\frac{\log \left(x\right)}{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left(x\right). The integral \int\frac{\log \left(x\right)}{x}dx results in: \frac{\ln\left(x\right)^2}{2\ln\left(10\right)}.
Solve the integral of logarithmic functions int((1+log(x))/x)dx
Final answer to the exercise
$\ln\left|x\right|+\frac{\ln\left|x\right|^2}{2\ln\left|10\right|}+C_0$