Choose the correct answer in Exercises 10 to 11.    Q10.    $\int \sqrt{1+x^2}dx$ is equal to                (A)    $\frac{x}{2}\sqrt{1+x^2} + \frac{1}{2}\log\left |\left(x + \sqrt{1+x^2} \right )\right| +C$                (B)    $\frac{2}{3}(1+x^2)^{\frac{3}{2}} + C$                (C)    $\frac{2}{3}x(1+x^2)^{\frac{3}{2}} + C$                (D)    $\frac{x^2}{2}\sqrt{1+x^2} + \frac{1}{2}x^2\log\left |x + \sqrt{1+x^2} \right| +C$

As we know that, $\int \sqrt{x^2+a^2}dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log|x+\sqrt{x^2+a^2}| +C$
So, $\int \sqrt{1+x^2}dx = \frac{x}{2}\sqrt{x^2+1}+\frac{1}{2}\log|x+\sqrt{x^2+1}| +C$