$\int\left(\frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}}\right) d x=$

• A

  $\frac{1}{2} \sqrt{1+\mathrm{x}}+\mathrm{c}$
• Correct answer
  B

  $\frac{2}{3}(1+\mathrm{x})^{3 / 2}+\mathrm{c}$
• C

  $\sqrt{1+x}+c$
• D

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

Hence, the correct answer is option: 'B'.