integrale di x^2 *cos^2(3x) integrale per parti reiterato

∫₀¹ x²(cos(3x))² dx

∫₀¹ x²(cos(3x))² dx = (cos(3x))² x³₃∣₀¹ + 6∫₀¹ cos(3x) sin(3x) x³₃ dx

f(x) = (cos(3x))²

f'(x) = 2cos(3x) (-sin(3x) ⋅ 3)

g(x) = x²

g(x) = x³₃

∫₀¹ x²(cos(3x))²dx = (cos(3x))² x³₃∣₀¹ + ∫₀¹ sin(6x) x² dx

f(x) = x³

f'(x) = 3x²

g'(x) = -sin(6x)

g(x) = -¹/₆ cos(6x)

∫₀¹x²(cos(3x))²dx = (cos(3x))²₃∣₀¹ + ∫₀¹ -x³₆ cos(6x)₁⁰ + ³/₆( cos<6x) x² dx)

f(x) = x²

f'(x) = 2x

g'(x) = cos(6x)

g(x) = ¹/₆ sin(x)

∫₀¹x²(cos(3x))²dx

f(x) = x

f'(x) = 1

g'(x) = -sin(6x)

g(x) = -¹/₆ cos(6x)

∫₀¹(x²(cos(3x))²dx = (cos(3x))²x³₁∣₀¹ + -x³₆ cos(6x)₁⁰ - ¹/₂²/₆ sin(6x)(x₆ cos(6x)₁⁰ + -¹/₆ ∫₀¹ cos(6x)dx)x²(cos(3x))² dx

∫₀¹ x²(cos(3x))² dx

∫₀¹ x²(cos(3x))² dx = (cos(3x))² ₀¹∫₀¹(cos(3x))² x³/3 ₀¹ + 1∫₀¹ sin(6x) x² dx

f(x) = (cos(3x))²

f'(x) = 2cos(3x) (-sin(3x) ⋅ 3)

g(x) = x²

g(x) = x³/3

∫₀¹ x²(cos(3x))² dx = (cos(3x))²x³/3 |₀¹ + 6∫₀¹ cos(3x)sin(3x) x³/3 dx= sin(6x) x³/3 dx

f(x) = x³

f'(x) = 3x²

g'(x) = -sin(6x)

g(x) = -1/6 cos(6x)

∫₀¹ x²(cos(3x))² dx = (cos(3x))² x³/3 |₀¹ + (x³/6 cos(6x)|₀¹ + 3/6) ∫₀¹ cos(6x) x² dx

f(x) = x²

f'(x) = 2x

g'(x) = cos(6x)

y(x) = 1/6 sin(x)

∫₀¹ x²(cos(3x))² dx = (cos(3x))² x³/3 |₀¹ + (-x³/6 cos(6x)|₀¹ + 1/2∫₀¹(x²/6 sin(6x) cos(6x)|₀¹ + 1/6) ∫₀¹ sin(6x) dx)

f(x) = x

f'(x) = 1

g'(x) = sin(6x)

g(x) = -1/6 cos(6x)

∫₀¹ x²(cos(3x))² dx = (cos(3x))² x³/3 |₀¹ + -x³/6 cos(6x)|₀¹ - 1/2 (x²/6 sin(6x) cos(6x)|₀¹ - 1/6) ∫∫₀¹ cos(x) dx