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∫ 3/⁵√x⁴ dx = ∫ 3.x^(4/5)   dx
= 3(5/9) x^(9/5) +c
= 15/9 x^(9/5) + c
= 15/9 x  ⁵√x⁴ + c

∫(x+4)(x-5) dx = ∫(x² - x  -20) dx
= 1/3 x³ - 1/2 x² - 20x + c

∫(x+2)²/(x²) dx = ∫ (x² + 4x +4)(x⁻²)  dx= ∫(1 + 4x⁻¹ + 4x⁻²) dx
= x- 4 ln x - 4 x⁻¹ + c
= x - 4 ln + 4/x + c

∫(x² -2)²/(x²)  dx = ∫(x⁴ - 4x² + 4)(x⁻²) dx
= ∫ (x² - 4+ 4x⁻²) dx
= 1/3 x³ - 4x - 4x⁻¹ + c
= 1/3 x³ - 4x - 4/x + c

∫ 3/(4x²) dx = ∫3/4 x⁻²  dx = 3/4 (-2) x⁻¹ +c
= - 3/(8x) + c

∫ 4/5 x^(-1/2) dx = 4/5 (2) x^(1/2) + c
= 8/5 √x + c