If $\int \frac{d x}{\sqrt{x+2}-\sqrt{x+1}}=\frac{2}{3}\left[(\lambda+1)^{\frac{3}{2}}+\lambda^{\frac{3}{2}}\right]+C$, then the value of λ is
Answer & explanation
Correct answer: option 3
$I=\int \frac{d x}{\sqrt{x+2}-\sqrt{x+1}}=\int(\sqrt{x+2}+\sqrt{x+1})dx$
$=\frac{2}{3}(x+2)^{\frac{3}{2}}+\frac{2}{3}(x+1)^{\frac{3}{2}}+C$
= x + 1