Evaluate the following : ∫ √(10 + x)/(10 - x).dx

Question

Evaluate the following :

\(\int \sqrt{\frac{10 + x}{10 - x}}.dx\)

∫ √(10 + x)/(10 - x).dx

Answer 1

∫ √(10 + x)/(10 - x).dx

= I₁ + I₂ .....(Let)

∴ -2x dx = dt

∴ 2x dx = -dt