Matematika

Pertanyaan

hasil dari integral
1. 3 cos 2x cos x dx
2. cos 7x cos 2x dx

1 Jawaban

  • ∫3cos 2x cos x dx
    = 3∫cos 2x dsin x
    = 3∫(1 - 2sin² x) dsin x
    = 3(∫dsin x - 2∫sin² x dx)
    = 3(sin x - (2/3)sin³ x) + c
    = 3sin x - 2sin³ x + c

    ∫cos 7x cos 2x dx
    = (1/2)(∫(cos 9x) dx + ∫(cos 5x) dx)
    = (1/2)(1/9)sin 9x + (1/2)(1/5)sin 5x + c
    = (1/18)sin 9x + (1/10)sin 5x + c

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