Integral (x pangkat 2 +2x) pangkat 2 / x dx

Jawaban yang benar adalah (1/4)x⁴ + (4/3)x³ + 2x² + c Ingat kembali: ∫ax^n dx = {a/(n+1)}·x^(n+1) + c ∫{f(x) + g(x)} dx = ∫f(x) dx + ∫g(x) dx Ingat juga: (a + b)² = a² + 2ab + b² (a + b)/c = (a/c) + (b/c) (a^m)^n = a^(m·n) (a^m)·(a^n) = a^(m+n) (ab)^m = (a^m)·(b^m) (a^m)/a = a^(m–1) ∫{(x² + 2x)²/x} dx = ∫[{(x²)² + 2·x²·2x + (2x)²}/x] dx = ∫[{x^(2·2) + 2·2·x^(2+1) + 2²·x²}/x] dx = ∫{(x⁴ + 4x³ + 4x²)/x} dx = ∫{(x⁴/x) + (4x³/x) + (4x²/x)} dx = ∫{x^(4–1) + 4x^(3–1) + 4x^(2–1)} dx = ∫(x³ + 4x² + 4x) dx = ∫x³ dx + ∫4x² dx + ∫4x dx = [{1/(3+1)}·x^(3+1) + c1] + [{4/(2+1)}·x^(2+1) + c2] + [{4/(1+1)}·x^(1+1) + c3] = (1/4)x⁴ + c1 + (4/3)x³ + c2 + (4/2)x² + c3 = (1/4)x⁴ + (4/3)x³ + 2x² + c1 + c2 + c3 = (1/4)x⁴ + (4/3)x³ + 2x² + c Jadi, hasil integral di atas adalah (1/4)x⁴ + (4/3)x³ + 2x² + c