Soal UNBK 2018 MTK IPA - no 15

Soal UNBK 2018 MTK IPA
Soal dan Pembahasan UNBK Matematika 2018
Jawaban UNBK Matematika 2018
Soal Matematika SMA 2018
Soal Ujian Akhir Matematika SMA 2018

15. Hasil dari ∫1/x² (3/x + 1)⁴ dx = ...

A. -3/5 (3/x + 1)⁵ + C
B. -1/15 (3/x + 1)⁵ + C
C. 1/15 (3/x + 1)⁵ + C
D. 1/5 (3/x + 1)⁵ + C
E. 3/5 (3/x + 1)⁵ + C

Jawaban : B
∫1/x² (3/x + 1)⁴ dx

U = 3/x + 1
dU = -3/x²dx
-1/3 dU = 1/x² dx

∫1/x² (3/x + 1)⁴ dx
= ∫ -1/3 (U)⁴ dU
= -1/3 . ∫U⁴ dU
= -1/3 . 1/5 . U⁵
= -1/15 (3/x + 1)⁵ + C

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