Question:medium
\( \int \frac{\sqrt{x^2 - 1}}{x} \, dx \) is equal to:
\( \int \frac{\sqrt{x^2 - 1}}{x} \, dx \) is equal to:
Show Hint
Trigonometric substitution turns algebraic radicals into powers of trig functions. Remember the triangle: if $\sec\theta = x/1$, the opposite side is $\sqrt{x^2-1}$.
Updated On: May 6, 2026
- \( \sqrt{x^2 - 1} - \sec^{-1} x + C \)
- \( \sqrt{x^2 - 1} + \tan^{-1} x + C \)
- \( \sqrt{x^2 - 1} + \sec^{-1} x + C \)
- \( \sqrt{x^2 - 1} - \tan x + C \)
- \( \sqrt{x^2 - 1} + \sec x + C \)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Methods of Integration
- The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
- MHT CET - 2025
- Mathematics
- Methods of Integration
The integral $ \int_0^1 \frac{1}{2 + \sqrt{2e}} \, dx $ is:
- MHT CET - 2025
- Mathematics
- Methods of Integration
- The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
- MHT CET - 2025
- Mathematics
- Methods of Integration
- Evaluate the integral \( \int x e^{x^2} dx \):
- BITSAT - 2025
- Mathematics
- Methods of Integration
- Want to practice more? Try solving extra ecology questions todayView All Questions
