$\int_0^{\mathrm{x}} \frac{\mathrm{t}^2}{\sqrt{\mathrm{a}^2+\mathrm{t}^2}} \mathrm{dt}=$

• A

  $\frac{x}{2} \sqrt{a^2+x^2}+\log \left|x+\sqrt{a^2+x^2}\right|$
• B

  $\sqrt{a^2+x^2}-a^2 \operatorname{Sinh}^{-1} \frac{x}{a}$
• C

  $\frac{x}{2} \sqrt{a^2+x^2}+\frac{a^2}{4} \log \left|x+\sqrt{a^2+x^2}\right|$
• Correct answer
  D

  $\frac{x}{2} \sqrt{a^2+x^2}-\frac{a^2}{2} \operatorname{Sinh}^{-1} \frac{x}{a}$

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