c = const (константа)
∫(x^6-2cosx)dx = ∫(x^6)dx - ∫(2cosx)dx = x^7/7 - 2sinx +c
∫(5/x^2-4sinx)dx = 5 ∫(x^(-2))dx -4 ∫(sinx)dx = -5*x^(-1) - 4*(-cosx) = -5/x + 4cosx +c
∫₉ ⁴ (3x^2-2x+5)dx = 3 ∫₉ ⁴ (x^2)dx - 2 ∫₉ ⁴ (x)dx + 5 ∫₉ ⁴ dx = x^3|₉⁴ - x^2 |₉⁴ + 5x |₉⁴ = 81-27-(16-9)+20-15 = 54-7+5 = 52
∫₉ ⁴ (x^4-3sinx)dx = ∫₉ ⁴(x^4)dx - 3 ∫₉ ⁴ (sinx)dx = x^5/5 |₉⁴ + 3cosx |₉⁴ = 4^5/5-3^5/5+3cos4-3cos3
∫₁ ² (3x^2+4x-3)dx = 3 ∫₁ ² (x^2)dx + 4 ∫₁ ² (x)dx - 3 ∫₁ ² dx = x^3|₁² +2x^2|₁² -3x |₁² = 8-1+8-2-6+3 = 10
∫(4/x^2+3sinx)dx = 4 ∫(x^(-2))dx +3 ∫(sinx)dx = -4/x -3cosx +c
∫₁ ⁴ (dx/√x) = ∫₁ ⁴(x^(-1/2))dx = 2x^(1/2)|₁⁴ = 2*2 - 2 = 2
∫₃ ⁰ (x^5+cosx)dx = ∫₃ ⁰(x^5)dx + ∫₃ ⁰(cosx)dx = x^6/6|₃⁰ + sinx|₃⁰ = -3^6/6 - sin3
∫₀ ³ (5x^4-2x)dx = 5 ∫₀ ³(x^4)dx - 2 ∫₀ ³(x)dx = x^5|₀³ -x^2 |₀³ = 3^5 - 3^2 = 9*26
∫(1/x^2-2cosx)dx = ∫ (x^(-2))dx - 2 ∫ (cosx)dx = -1/x - 2sinx +c
∫(x^3-2sinx)dx = ∫ (x^3)dx - 2 ∫ (sinx)dx = x^4/4 + 2cosx +c
∫(7x^6+5x^4-2)dx = 7 ∫(x^6)dx + 5 ∫ (x^4)dx - 2 ∫ dx = x^7+x^5 - 2x +c
∫(3/x^2+5cosx)dx = 3 ∫(x^(-2))dx + 5 ∫(cosx)dx = -3/x + 5sinx +c
9 от 6 = 9/6 = 150%