TS EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{\left(x^2-a^2\right)^{\frac{3}{2}}}\) is equal to
- A \(\frac{a^2 x}{\sqrt{\left(x^2-a^2\right)}}+C\)
- B \(-\frac{1}{a^2}\left(x^2-a^2\right)^{\frac{5}{2}}+C\)
- C \(-\frac{x}{a^2 \sqrt{\left(x^2-a^2\right)}}+C\)
- D \(\frac{1}{a^2 \sqrt{\left(x^2-a^2\right)}}+C\)
Answer & Solution
Correct Answer
(C) \(-\frac{x}{a^2 \sqrt{\left(x^2-a^2\right)}}+C\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{d x}{\left(x^2-a^2\right)^{3 / 2}}\) Putting \(x=a \sec \theta \Rightarrow d x=a \sec \theta \cdot \tan \theta d \theta\)…
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