Question

How to determine the indefinite integral of e^square rootx/square rootx (substitution or parts) ?

Accepted Answer

We have to find the integral of e^ sqrt x / sqrt x.
Let u = sqrt x
=> du/dx = 1/2* sqrt x
=> 2* du = dx / sqrt x
Int [ (e^ sqrt x / sqrt x) dx]
=> Int [ e^u * (dx/sqrt x)]
=> Int [ e^u * 2 du]
=> 2*e^u + C
replace u = sqrt x
=> 2e^ sqrt x + C
Therefore the required integral is 2*e^ sqrt x + C

Answer

We'll integrate using substitution or we'll change the variable. For this reason, we'll consider the formula:
We'll note sqrtx = t.
We'll differentiate both sides:
dx/2sqrtx = dt
dx/sqrtx = 2dt
We'll re-write the integral in t:
Int e^t*2dt = 2e^t + C
We'll substitute t by sqrt x:
Int e^sqrtx*dx/sqrtx = 2e^sqrtx + C
The indefinite integral is evaluated using substitution and the result is:
Int e^sqrtx*dx/sqrtx = 2e^sqrtx + C

Calculus

How to determine the indefinite integral of e^square rootx/square rootx (substitution or parts) ?

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