AP EAMCET · Maths · Indefinite Integration
If \(\frac{1}{(3-5 x)(2+3 x)}=\frac{A}{3-5 x}+\frac{B}{2+3 x}\), then \(A+B\) is equal to
- A \(\frac{7}{19}\)
- B \(\frac{8}{19}\)
- C \(\frac{9}{19}\)
- D \(\frac{10}{19}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{19}\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{1}{(3-5 x)(2+3 x)}=\frac{A}{3-5 x}+\frac{B}{2+3 x}\) \(\frac{1}{(3-5 x)(2+3 x)}=\frac{2 A+3 A x+3 B-5 B x}{(3-5 x)(2+3 x)}\) \(\Rightarrow \quad 1=x(3 A-5 B)+(2 A+3 B)\) \(3 A-5 B=0\) ...(i) and \(\quad 2 A+3 B=1\) ...(ii) Eq. (i) \(\times 3+\) Eq. (ii)…
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