Note: Example 3.29 as well as "the General Method" from the textbook Links to an external site. might help you with this question.    Problem: Evaluate the integral ∫ x+4 (x+2)(x−4) dx     A student hands in the following 'solution'. Is it correct? Line 1: Let's use the method of Partial Fractions. The degree of the numerator is less than the degree of the denominator, so we do not need to use long division.  Line 2: There are two distinct (=different) linear factors so the partial fraction decomposition is of the form: Line 3: x+4 (x+2)(x−4) = A x+2 + B x−4     for some constants A  and B.  Line 4: Multiply both sides by (x+2)(x−4):  Line 5: x+4=A(x−4)+B(x+2)   Line 6: Simplify: x+4=Ax−4A+Bx+2B  Line 7: The number of x on the two sides must be equal. Also, the constants on both sides must be equal:     A+B=1              −4A+2B=4  Line 8: The first equation becomes B=1−A  which can be inserted into the second equation:  Line 9: −4A+2(1−A)=4⟹−4A+2−2A=4⟹−6A=2⟹A=− 1 3   Line 10: Therefore B=1−(− 1 3 )= 4 3   Line 11: Now we know the values of A and B so we can continue with the integral: Line 12: ∫ x+4 (x+2)(x−4) dx=∫( 4 3(x+2) − 1 3(x−4) )dx=      Line 13: =∫ 4 3(x+2) dx−∫ 1 3(x−4) dx=      Line 14: = 4 3 ln|x+2|− 1 3 ln|x−4|+C         Is the solution correct, or if not, in which line does the first error occur? [line]