Question

\(\int \sqrt{1+x^2}dx\) is equal to

• A. \(\frac{x}{2}\sqrt{1+x^2}+\frac{1}{2}\log\mid x+\sqrt{1+x^2}\mid +C\)
• B. \(\frac{2}{3}(1+x^2)^{\frac{2}{3}}+C\)
• C. \(\frac{2}{3}x(1+x^2)^{\frac{3}{2}}+C\)
• D. \(\frac{x^2}{2}\sqrt{1+x^2}+\frac{1}{2}x^2\log\mid x+\sqrt{1+x^2}\mid+C\)

Answer 1

The Correct Option is A

It is known that,\(\int \sqrt{a^2+x^2}dx = \frac{x}{2}\sqrt{a^2+x^2}+\frac{a^2}{2}\log\mid x+\sqrt{x^2+a^2}\mid+C\)

∴\(\int \sqrt{1+x^2}dx=\frac{x}{2}\sqrt{1+x^2}+\frac{1}{2}\log\mid x+\sqrt{1+x^2}\mid+C\)

Hence, the correct answer is A.