Try Out 3 Matematika IPA 2019 no 30

Try Out Matematika IPA 2019
Soal dan Pembahasan Try Out Matematika IPA 2019
Jawaban Try Out Matematika IPA 2019
Try Out Ujian Matematika SMA IPA

30. Hasil dari ∫ (x² + 2) / √(x³ + 6x + 1) dx = ...

A. 1/3 √(x³ + 6x + 1) +C
B. 2/3 √(x³ + 6x + 1) + C
C. √(x³ + 6x + 1) + C + C
D. 2√(x³ + 6x + 1) + C
E. 3√(x³ + 6x + 1) + C



Jawaban : 
U = x³ + 6x + 1
dU = 3x² + 6 dx
dU = 3(x² + 2) dx
1/3 dU = (x² + 2) dx

 ∫ (x² + 2) /√(x³ + 6x + 1) dx
= ∫ 1/3 . 1/√U dU
= 1/3 ∫ (U)^-1/2 dU
= 1/3 . 2(U)^1/2 + C
= 2/3 √(x³ + 6x + 1) + C

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