What is the function y if dy/dx=(e^lnx)/x?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function y has to be determined given that dy/dx = (e^lnx)/x

y = Int [ (e^ln x)/x dx]

let ln x = z

dz = dx/x

=> Int [ e^z dz]

=> e^z + C

substitute z = ln x

=> e^(ln x) + C

The function y = e^(ln x) + C

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the original function, we'll have to evaluate the indefinite integral of dy.

We'll replace ln x by t.

ln x = t

We'll differentiate both sides and we'll get:

dx/x = dt

We'll re-write the integral in the changed variable:

Int (e^ln x) dx/ x  = Int e^t*dt

Int e^t*dt = e^t + C

The primitive function is: y =  e^ln x + C

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