∫(x+1)(x62 + 2x + 3)^3 dx = . . .

1/8 (x² + 2x + 3)⁴ + C

Pembahasan

∫ (x + 1) (x² + 2x + 3)³ dx

misal

u = x² + 2x + 3

du = 2x + 2

dx = du/ 2 (x + 1)

∫ (x + 1) . u³ . du/ 2 (x + 1)

1/2 . ∫ u³ . du

= 1/2 . 1/(3 + 1) . u³⁺¹

= 1/2 . 1/4 . u⁴

= 1/8 . u⁴ + C

= 1/8 (x² + 2x + 3)⁴ + C

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Detil Jawaban

Kelas: 11

Mapel: Matematika

Bab: Integral Tak Tentu

Kode: 11.2.10

Kata Kunci: integral substitusi

Jawaban:

• Integral

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