Integrate the function below. Show All Steps

Question

Integrate the function below. Show All Steps. If possible attach a video going through the problem

Answer 1

To get the antiderivative (also called the primitive or indefinite integral):

1) multiply the integral by 3/2 and the integrand by 2/3

2) add 8 to the numerator and subtract 20/3 over the same denominator as a separate integral

3) the first piece now integrates by u substitution

4) complete the square in the denominator of the other piece and integrate as an arctan

I have given you the "steps"....you do the problem by following the steps!

Answer 2

(3x+2)/(x²+8x+11)

can be decomposed with partial fraction method.

(3x+2)/(x²+8x+11)=(-√5+3/2)/(x-[-4+√5])+(√5+3/2)/(x-[-4-√5])

∫[(-√5+3/2)/(x-[-4+√5])+(√5+3/2)/(x-[-4-√5])]dx

=(-√5+3/2)ln|x-[-4+√5]|+(√5+3/2)ln|x-[-4-√5]|+C

there is absolute values for variable expression for ln since x is allowed to be negative numbers