Question

\[ \int \frac{dx}{\sqrt{x+1}+\sqrt{x}}= \]

• A. \(\frac{2}{3}\left[(x+1)^{\frac{3}{2}}-x^{\frac{3}{2}}\right]+c\)
• B. \(\frac{2}{3}\left[(x+1)^{\frac{3}{2}}+x^{\frac{3}{2}}\right]+c\)
• C. \(\frac{3}{2}\left[(x+1)^{\frac{3}{2}}-x^{\frac{3}{2}}\right]+c\)
• D. \(\frac{3}{2}\left[(x+1)^{\frac{3}{2}}+x^{\frac{3}{2}}\right]+c\)

Hint:

For integrals with \(\sqrt{x+1}+\sqrt{x}\) in the denominator, rationalize using \(\sqrt{x+1}-\sqrt{x}\).

Answer 1

The Correct Option is A