Integral logarithmic calculus math help.

Question

Pls find ∫x^(2+x)log_x2dx

I dont know how to do calculus of a logs base, here x is the base of the log.

Answer 1

Via the properties of natural log and e, we know that log_a(x) = ln(x)/ln(a), but it also works if a and x swap positions, in that log_x(a) = ln(a)/ln(x) is also true. Replace log_x(2) with (ln(2)/ln(x)) and solve. I'm assuming since you specified which type of log_base integral you did not know how to solve that you DO know how to deal with the integral of ln.