Tolong bantu jawab integral dan jangan spam

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Pertanyaan :


Tolong bantu jawab integral dan jangan spam

Jawaban :

∫x⁵√(-x³+2) dx

misal,

u = -x³ + 2
du = -3x² dx
dx = du/(-3x²)

u = -x³ + 2
x³ = 2 – u

∫x⁵√(-x³+2) dx = ∫x⁵√u du/(-3x²)
= ∫x³√u du/(-3)
= ∫(2 – u)√u du/(-3)
= ∫-(2 – u)√u du/3
= (1/3)∫(u – 2)√u du
= (1/3)∫u.√u – 2√u du
= (1/3)((2/5)u²√u – (4/3)u.√u)
= (2/15)u²√u – (4/3)u√u
= ((2/15)u² – (4/3)u )√u
= ((2/15)(-x³ + 2)² – (4/3)(-x³ + 2))√(-x³ + 2)

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