Evaluate using long division first to write f(x) as the sum of a polynomial and a proper rational function. int (xdx)/(3x-4)

piopiopioirp

piopiopioirp

Answered question

2022-11-19

Evaluate using long division first to write f(x) as the sum of a polynomial and a proper rational function.
x d x 3 x 4

Answer & Explanation

avuglantsaew

avuglantsaew

Beginner2022-11-20Added 15 answers

The required is to evaluate the integral.
x ( 3 x 4 ) d x
By using the long division:
x ( 3 x 4 ) = 1 3 + 4 3 ( 3 x 4 )
x ( 3 x 4 ) d x = 1 3 d x + 4 3 ( 3 x 4 ) d x
= 1 3 d x + 4 3 3 1 3 ( 3 x 4 ) d x
= 1 3 d x + 4 9 3 ( 3 x 4 ) d x
= 1 3 x + 4 9 ln | 3 x 4 | + C
Result:
x ( 3 x 4 ) d x = 1 3 x + 4 9 ln | 3 x 4 | + C

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