TS EAMCET · Maths · Indefinite Integration
\(\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=\)
- A \(\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)
- B \(-\frac{4}{5} \log |\cos 3 x+2 \sin 3 x|+\frac{7 x}{5}+c\)
- C \(\frac{7}{5} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)
- D \(-\frac{8}{15} \log |\cos 3 x+2 \sin 3 x|+\frac{x}{5}+c\)
Answer & Solution
Correct Answer
(A) \(\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)
Step-by-step Solution
Detailed explanation
\(\frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x}\) \(\begin{aligned} & =\frac{A(\cos 3 x+2 \sin 3 x)+B(6 \cos 3 x-3 \sin 3 x)}{\cos 3 x+2 \sin 3 x} \\ & =\frac{(A+6 B) \cos 3 x+(2 A-3 B) \sin 3 x}{\cos 3 x+2 \sin 3 x} \\ & A+6 B=2 ; 2 A-3 B=-3 \end{aligned}\) After solving we…
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