∫ (1 + x √(x + x^2))/(√x + √1 + x)

Question

\(\int \frac{1 + x \sqrt{x + x^2}}{\sqrt{x} + \sqrt{1 + x}}.dx =\)

∫ (1 + x √(x + x²))/(√x + √1 + x)

(a) \(\frac{1}{2} \sqrt{x + 1} + c\)

(b) \(\frac{2}{3} (x + 1) ^{\frac{3}{2}}+ c\)

(c) \(\sqrt{x + 1} + c\)

(d) \(2 (x + 1) ^{\frac{3}{2}}+ c\)

Answer 1

Correct answer is (b) \(\frac{2}{3} (x + 1) ^{\frac{3}{2}}+ c\)