Question

Integral of $f\left(x\right)=\sqrt{1+x^2}$ with respect to $x^2$ is

• A. $\frac{2}{3}\frac{{(1+x^2)}^{3/2}}{x}+k$
• B. $\frac{2}{3}{(1+x^2)}^{3/2}+k$
• C. $\frac{2}{3}x{(1+x^2)}^{3/2}+k$
• D. None of these

Answer 1

Answer: (B)

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

$f\left(x\right)=\sqrt{1+x^2}$

$\int \sqrt{1+x^2}d{x}^2$

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

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