The integration of logx.

Find the integrating factor of the given differential equation: ydx-xdy+(logx)dx=0

Find the integrating factor of the differential equation: x log x (dy)/(dx)+y=(2)/(x)logx, x gt 1

Evaluate the following definite integral: int_1^e(logx)/x dx

Evaluate the following definite integral: int_1^2logx\ dx

Evaluate the following definite integral: int_1^3(logx)/((x+1)^2)dx

The value of the integral int(e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))dx is equal to (A) x^2+c (B) x^3/3+c (C) x^2/2+c (D) none of these

The value of the integral int(e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))dx is equal to (A) x^2+c (B) x^3/3+c (C) x^2/2+c (D) none of these

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: inte^x x^x(2+logx)= (A) e^x x^xlogx+C (B) e^x+x^x+C (C) e^x x(logx)^2+C (D) e^x.x^x+C

If f(x)=logx , then the derivative of f (logx)w.r.t.x is