Tìm nguyên hàm ∫cos5xcos3xdx.

Question

Tìm nguyên hàm \(\int \cos 5x\cos 3xdx .\)
 

A. \(\frac{1}{8} \sin 8x+\frac{1}{2} \sin 2x+C. \)

B. \(\frac{1}{2} \sin 8x+\frac{1}{2} \sin 2x+C.\)

C. \(\frac{1}{16} \sin 8x+\frac{1}{4} \sin 2x+C. \)

D. \(\frac{-1}{16} \sin 8x+\frac{-1}{4} \sin 2x+C. \)

Answer 1

Chọn C

Ta có:

 \(\int \cos 5x\cos 3xdx=\int \frac{1}{2} \left(\cos 8x+\cos 2x\right)dx\)

\(=  \frac{1}{16} \sin 8x+\frac{1}{4} \sin 2x+C\)

Do đó, ta chọn C.