How do you evaluate the definite integral $\int e^{ln x + 2}$ $inte^(lnx+2)$ from $[1, 2]$ $[1,2]$ ?

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Answer 1 · 2018-05-09T23:27:16

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

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:

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

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

$\ \ = (3e^2)/2$

$\ \ ~~ 11.083584 ...$

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