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Yuka21yuka
@Yuka21yuka
July 2022
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Вычислить неопределенный интеграл [tex] \int\limits[/tex](5x-1)cos3xdx
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Lesben
∫uv´=uv-∫u´v (per partes)
u=5x-1, u´=5
v´=cos3x, v=∫cos3xdx=(sin3x)/3
∫(5x-1)cos3xdx=(5x-1)(sin3x)/3 -∫5(sin3x)/3dx=
=(5x-1)(sin3x)/3+5(cos3x)/3 + c
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Answers & Comments
u=5x-1, u´=5
v´=cos3x, v=∫cos3xdx=(sin3x)/3
∫(5x-1)cos3xdx=(5x-1)(sin3x)/3 -∫5(sin3x)/3dx=
=(5x-1)(sin3x)/3+5(cos3x)/3 + c