Question

$\int \frac{\sqrt{\sqrt{x} + 1}}{\sqrt{x}} dx = $}

• A. $\frac{4}{3} (\sqrt{x} + 1)^{3/2} + C$
• B. $\frac{2}{3} (\sqrt{x} + 1)^{3/2} + C$
• C. $\frac{4}{3} (\sqrt{x} + 1)^{3/4} + C$
• D. $\frac{1}{3} (\sqrt{x} + 1)^{3/2} + C$
• E. $\frac{3}{4} (\sqrt{x} + 1)^{3/2} + C$

Hint:

Whenever you see \( \sqrt{x} \) in a denominator and another \( \sqrt{x} \) inside another root, substitution is almost always the intended path. The \( 1/2 \) from the derivative often converts to a factor of 2 in the numerator.

Answer 1

The Correct Option is A