Question

What's The integral 3/x from 1 to e? And why?

Answer 1

u = 1+3e-x 

so that (Don't forget to use the chain rule on e-x.)

du = 3e-x(-1) dx = -3e-x dx , 

or

(-1/3)du = e-x dx . 

However, how can we replace the term e-3x in the original problem ? Note that

 . 

From the u-substitution

u = 1+3e-x , 

we can "back substitute" with

e-x = (1/3)(u-1) . 

Substitute into the original problem, replacing all forms of x, getting

 

(Recall that (AB)C = AC BC .)

Answer 2

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