hasil f(2x -1 ) (x^2 - x + 5)^3 dx adlah

Bab Integral
Matematika SMA Kelas XII

∫(2x - 1) (x² - x + 5)³ dx = ...

u = x² - x + 5
(du / dx) = 2x - 1

du = (2x - 1) . dx

∫(2x - 1) . (x² - x + 5)³ dx = ∫ u³ . du
∫(2x - 1) . (x² - x + 5)³ dx = 1/4 . u⁴ + C
∫(2x - 1) . (x² - x + 5)³ dx = (1/4) . (x² - x + 5)⁴ + C 

[tex]\displaystyle \text{misal :}\\x^2-x+5=u\\2x-1\,dx=du\\\\\int(2x-1)(x^2-2x+5)^3\,dx=\int(x^2-2x+5)^3(2x-1)\,dx\\\int(2x-1)(x^2-2x+5)^3\,dx=\int u^3\,du\\\int(2x-1)(x^2-2x+5)^3\,dx=\frac14u^4+C\\\boxed{\boxed{\int(2x-1)(x^2-2x+5)^3\,dx=\frac14(x^2-x+5)^4+C}}[/tex]