∫ (x)/√(1 - x^2​​​​​​​) dx = ?

Question

Mark (√) against the correct answer in each of the following:

\(\int \frac{x}{\sqrt{1-x^2}}dx = ?\)

∫ (x)/√(1 - x²) dx = ?

A. \(\text{sin}^{-1}x + C\)

B. \(\text{sin}^{-1}\sqrt{x} + C\)

C. \(\sqrt{1 - x^2} + C\)

D. \(-\sqrt{1 - x^2} + C\)

Answer 1

Given = \(\int \frac{x}{\sqrt{1-x^2}}dx\)

∫ (x)/√(1 - x²) dx

Let, 1 – x² = z²

⇒ - 2x dx = 2z dz

So,

where c is the integrating constant.