How to integrate the function y=e^(square root x)/square root x?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to integrate y = e^(sqrt x)/sqrt x

Int[e^(sqrt x)/sqrt x dx]

let sqrt x = t, 2*dt = (1/sqrt x) dx

=> Int[e^t 2*dt]

=> 2*e^t + C

substitute t = sqrt x

=> 2*e^(sqrt x) + C

The required integral is 2*e^(sqrt x) + C

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use the substitution technique to evaluate the indefinite integral of the given function.

Let `sqrt(x)` = t => dx/2`sqrt(x)` = dt => dx/`sqrt(x)` = 2dt

`int` e^(`sqrt(x)` ) dx/`sqrt(x)` = 2`int` e^t dt

2`int` e^t dt = 2 e^t + C

`int` e^`sqrt(x)` dx/`sqrt(x)` = 2e^`sqrt(x)` + C

The requested indefinite integral of the given function is `int` e^`sqrt(x)` dx/`sqrt(x)` = 2e^`sqrt(x)` + C.

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