Question

Evaluate : `int ("x" + 1)/("x"("x" + log"x")`dx

Answer 1

Let I = `int ("x" + 1)/("x"("x" + log"x")`dx

= `int (("x" + 1)/"x")/("x" + log"x")`dx

= `int (1 + 1/x)/(x + logx)` dx

= `int [(d/dx)(x + logx)]/(x + logx)` dx

= log |x + log x| + c

`(int f(x)/f(x) dx = log |f(x)| + c)`