Question

The value of $\int \frac{{\sin }^{8}x-{\cos }^{8}x}{1-2{\sin }^{2}x{\cos }^{2}x}dx$ is :

• A. $\frac{1}{2}\sin 2x+C$
• B. $-\frac{1}{2}\sin 2x+C$
• C. $-\frac{1}{2}\sin x+C$
• D. $-{\sin }^{2}x+C$

Answer 1

Answer: (B)

$\int \frac{{\sin }^{8}x-{\cos }^{8}x}{{\sin }^{4}x+{\cos }^{4}x}dx=\int \left({\sin }^{4}x-{\cos }^{4}x\right)dx=\int \left({\sin }^{2}x-{\cos }^{2}x\right)dx=-\frac{1}{2}\sin 2x+C$