What's the integral 3/x from 1 to e? and why?

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 .)

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

a and c

step-by-step explanation: