Question

$\displaystyle \int \sqrt{1 + \sin\left(\frac{x}{8}\right)} \, dx =$

• A. $16\sin\left(\frac{x}{32}\right) - 16\cos\left(\frac{x}{32}\right) + C$
• B. $16\sin\left(\frac{x}{16}\right) - 16\cos\left(\frac{x}{16}\right) + C$
• C. $16\sin\left(\frac{x}{32}\right) + 16\cos\left(\frac{x}{32}\right) + C$
• D. $16\sin\left(\frac{x}{16}\right) + 16\cos\left(\frac{x}{16}\right) + C$
• E. $8\sin\left(\frac{x}{16}\right) - 8\cos\left(\frac{x}{16}\right) + C$

Hint:

Use $1+\sin\theta$ identity to convert root into linear trig form.

Answer 1

The Correct Option is B