Nilai dari ʃ cos^4 2x sin 2x dx = ….

Nilai dari ʃ cos4 2x sin 2x dx = ….
A. −1/10 sin52x + C
B. −1/10 cos52x + C
C. −1/5 cos52x + C
D. 1/5 cos52x + C
E. 1/10 sin52x + C

Jawab: C

Misal:
u = cos 2x
du = -2 Sin 2x dx
sin 2x dx = −1/2du

Menentukan nilai intergal fungsi trigonometri:
ʃ cos4 2x sin 2x dx = 1/2 ʃ u4 du
= −1/2 × 1/5u5 + C
= −1/10 u5 + C
= −1/10 cos52x + C

Jadi, nilai dari ʃ cos4 2x sin 2x dx = −1/10 cos52x + C

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