Integral x^2 3 akar 1- x^3 dx
Matematika
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Pertanyaan
Integral x^2 3 akar 1- x^3 dx
1 Jawaban
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1. Jawaban arsetpopeye
Integral x^2 (1 - x^3)^(1/3) dx
Misal
u = 1 - x^3
du = -3x^2 dx => dx = du/(-3x^2)
Integral x^2 . u^(1/3) du/(-3x^2)
= Integral -1/3 u^(1/3) du
= (-1/3)/(4/3) u^4/3 + C
= -1/4 (1 - x^3)^(4/3) + C
= -1/4 (^3√(1 - x^3)^4) + C
= -1/4 (1 - x^3) (^3√(1 - x^3)) + C