Exercise
$\int-x.\log\left(\frac{c}{x}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(-xlog(c/x))dx. The integral of a function times a constant (-1) is equal to the constant times the integral of the function. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Multiplying the fraction by x. Take the constant \frac{1}{\ln\left|10\right|} out of the integral.
Solve the integral of logarithmic functions int(-xlog(c/x))dx
Final answer to the exercise
$\frac{-\left(\left(\frac{1}{2}\ln\left|c\right|-\frac{1}{2}\ln\left|x\right|\right)x^2+\frac{1}{4}x^2\right)}{\ln\left|10\right|}+C_0$