AP EAMCET · Maths · Indefinite Integration
If \(\frac{2 x^2+5 x+6}{(x+2)^3}=\frac{a}{x+2}+\frac{b}{(x+2)^2}+\frac{c}{(x+2)^3}\) then \(\mathrm{a} . \mathrm{b}+\mathrm{b} . \mathrm{c}+\mathrm{c} . \mathrm{a}=\)
- A 28
- B 14
- C -10
- D -8
Answer & Solution
Correct Answer
(C) -10
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Given } \frac{2 x^2+5 x+6}{(x+2)^3}=\frac{a}{(x+2)}+\frac{b}{(x+2)^2}+\frac{c}{(x+3)^3} \\ & \Rightarrow 2 x^2+5 x+6=a(x+2)^2+b(x+2)+c \\ & \Rightarrow 2 x^2+5 x+6=x^2(a)+x(4 a+b)+(4 a+2 b+c) \end{aligned} \] Comparing we get, \[ a=2, b=-3, c=4 \]…
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