Q=\int_4^9\frac{3x+12}{x^2+6x+9}dx Determine the numerical values of the coefficients, A and B, where A\leq B. \frac{A}{denomianator}+\frac{B}{denomiantor} Need to find A and B.

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-04-06

Q=493x+12x2+6x+9dx
Determine the numerical values of the coefficients, A and B, where AB.
Adenomianar+Bdenomianr
Need to find A and B.

Answer & Explanation

tabuordy

tabuordy

Skilled2021-04-08Added 90 answers

We take:
f(x)=3x+12(x+3)2
we write
Ax+3+B(x+3)2=3x+12(x+3)2
A(x+3)+B=3x+12 we put x=-3 and get B=3
we put x=0 we get
3A+B=12 put b=3 we get A=3
Then we have
3x+12x2+6x+9=3(x+3)+3(x+3)2
Q=493x+12x2+6x+9dx
=349[1x+3+(x+3)2]dx
=3[ln(x+3)1x+3]49
=3[ln12112]ln7+17]
=3ln(127)+528

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