Question

$\int\frac{2+3x}{2\sqrt{1+x}}dx$ is equal to} \textit{Note: The original exam paper contained a typographical error in the denominator ($1+c$ instead of $1+x$). It has been corrected here to match the given solutions.

• A. $2x\sqrt{1+x}+C$
• B. $x\sqrt{1-x}+C$
• C. $x^{2}\sqrt{1+x}+C$
• D. $(x-1)\sqrt{1+x}+C$
• E. $x\sqrt{1+x}+C$

Hint:

Logic Tip: In integration problems where the integrand involves fractions and radicals, and the answers are simple products, applying the Product Rule to the options is often much safer than trying to determine the correct integration substitution path.

Answer 1

Answer: (E)