How do you evaluate the definite integral #inte^(lnx+2)# from #[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 ... #