Evaluate using long division first to write f(x) as the sum of a polynomial and a proper rational function. int ((x^2 + 2)dx)/(x+3)

misyjny76

misyjny76

Answered question

2022-09-25

Evaluate using long division first to write f(x) as the sum of a polynomial and a proper rational function.
( x 2 + 2 ) d x x + 3

Answer & Explanation

asijikisi67

asijikisi67

Beginner2022-09-26Added 10 answers

The required is to evaluate the integral..
x 2 + 2 x + 3 d x
By using the long division:
x 2 + 2 x + 3 = ( x 3 ) + 11 x + 3
x 2 + 2 x + 3 d x = x d x 3 d x + 11 x + 3 d x
= x 2 2 3 x + 11 ln | x + 3 | + C
= 1 2 [ x 2 6 x + 22 ln | x + 3 | ] + C
Result:
x 2 + 2 x + 3 d x = 1 2 [ x 2 6 x + 22 ln | x + 3 | ] + C

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