Question

Kuis
(medium-susah)
Tentukan hasil dari
integral berikut ini:

[tex]\rm\int (-\frac{12}{x^4})(\frac{4}{x^3}+7)~dx=....[/tex]

Answer 1

Penjelasan dengan langkah-langkah:

ʃ (-12/x⁴) (4/x³ + 7) dx

ʃ (-12/x⁴) ((4 + 7x³)/x³) dx

ʃ -12(4+7x³)/ x⁷ dx

ʃ (-48 - 84x³)/x⁷ dx

ʃ x^-7 (-48 - 84x³) dx

ʃ -48x^-7 - 84x^(3-7) dx

ʃ -48x^-7 - 84x^-4 dx

= -48x^(-7+1)/(-7+1) - 84x^(-4+1)/(-4+1) + C

= -48x^(-6)/(-6) - 84x^(-3)/(-3) + C

= (-48)/(-6)x^-6 - (84)/(-3) x^-3 + C

= 8x^-6 + 28x^-3 + C

= 8/x⁶ + 28/x³ + C