How do you evaluate the definite integral inte^(lnx+2)elnx+2 from [1,2][1,2]?

1 Answer
May 9, 2018

int_1^2 \ e^(lnx+2) \ dx = (3e^2)/2

Explanation:

We seek:

I = int_1^2 \ e^(lnx+2) \ dx

Using the properties of exponents:

I = int_1^2 \ e^(lnx)e^(2) \ dx

\ \ = e^2 \ int_1^2 \ x \ dx

Which we can readily integrate using the power rule, so that:

I = e^2 \ [ x^2/2 \ ]_1^2

\ \ = e^2 (4/2-1/2)

\ \ = (3e^2)/2

\ \ ~~ 11.083584 ...