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∫sin4(x)cos5(x)dx
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Solution
sin5(x)5−2sin7(x)7+sin9(x)9+C
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Solution steps
Solve by:
One step at a time
∫sin4(x)cos5(x)dx
Riscrivere utilizzando identità trigonometriche
=∫(1−sin2(x))2cos(x)sin4(x)dx
Applicare la sostituzione u:∫u4(1−u2)2du
=∫u4(1−u2)2du
Espandi u4(1−u2)2:u4−2u6+u8
=∫u4−2u6+u8du
Applica la Regola della Somma: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx