What is the best method to evaluate the integral of the quotient of the quantity x squared plus 5 times x plus and the quantity x plus 1 dx ?

Question

What is the best method to evaluate  ?

A	Integration by parts
B	Rewrite the integral using long division
C	Rewrite the integral using partial fractions
D	Use a substitution

Answer 1

Option B: Rewrite the integral using long division

x + 4

________________

x+1 | x^2 + 5 x + 6

x^2 + x

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4 x + 6

4 x + 4

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2

x+4 + 2/(x+1)

(1/2)x^2 + 4x + 2 ln |x+1|