. Given f(x) = e 2x e 2x + 3e x + 2 : (a) Make the substitution u = e x to convert Z f(x) dx into an integral in u (HINT: The easiest way to do this in Python is to substitute into f(x) u 0 (x) ) (b) Your result from part (a) should be a rational function in u. Find the partial fraction decomposition (directly in Python) and use it to integrate the function. (Remember to substitute x back in when done!) (c) Evaluate Z f(x) dx directly.

Step-by-step explanation:

Given;

a)

substitute

b)

Apply partial fraction in (a), we get;

where C is an arbitrary constant

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation: