Evaluate the following integral. integral from nothing to nothing startfraction 3 e superscript x over e superscript 2 x baseline plus 2 e superscript x baseline plus 1 endfraction dx∫ 3ex e2x+2ex+1dx integral from nothing to nothing startfraction 3 e superscript x over e superscript 2 x baseline plus 2 e superscript x baseline plus 1 endfraction dx∫ 3ex e2x+2ex+1dxequals

Step-by-step explanation:

To find this integral you must:

1. Take the constant out:

2. Factor

3. Apply u-substitution

4. Apply the Power Rule

5. Substitute back

6. Add a constant to the solution

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is