AP EAMCET · Maths · Indefinite Integration
\(\int \frac{(3 x-2) \tan \left(\sqrt{9 x^2-12 x+1}\right)}{\sqrt{9 x^2-12 x+1}} d x=\)
- A \(\frac{1}{3} \sec ^2 \sqrt{9 x^2-12 x+1}+c\)
- B \(\frac{1}{3} \sec ^2 x+c\)
- C \(\frac{1}{2} \log \left|\sec \sqrt{9 x^2-12 x+1}\right|+c\)
- D \(\frac{1}{3} \log \left|\sec \sqrt{9 x^2-12 x+1}\right|+c\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3} \log \left|\sec \sqrt{9 x^2-12 x+1}\right|+c\)
Step-by-step Solution
Detailed explanation
Let \(u = \sqrt{9x^2 - 12x + 1}\) \(2u \, du = (18x - 12) \, dx \Rightarrow (3x - 2) \, dx = \frac{u}{3} \, du\) \(\int \frac{\tan(u)}{u} \cdot \frac{u}{3} \, du = \frac{1}{3} \int \tan(u) \, du\) \(= \frac{1}{3} \log|\sec(u)| + C\)…
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