Selesaikan dengan substitusi trigonometri : ∫ ( (x^2) / √(9 - x^2 ) ) dx= .... Mohon bantuannya mastah. Terima kasih

Misal, x = 3sin t
sin t = x/3
t = arcsin(x/3)

x² = (3sin t)² = 9sin²t

dx = 3 cos t dt

∫(x²)/√(9 - x²) dx = ∫(x²)/√(9 - 9sin²t) dx
= ∫(x²)/√(9(1 - sin²t)) dx
= ∫(x²)/√(9cos²t) dx
= ∫(x²)/3cost dx
= ∫9sin²t/3cost * (3 cost dt)
= ∫9sin²t dt
= ∫9(1 - cos 2t)/2 dt
= (9/2)∫(1 - cos2t) dt
= (9/2)(t - (1/2)sin2t) + C
= (9/2)t - (9/4)sin2t + C

sin2t = 2.sint.cost
sin t = x/3
cost = √(3² - x²)/3
2.sint.cost = 2.(x/3)(√(3² - x²)/3
= (2x√(3² - x²))/9

(9/2)t - (9/4)sin2t + C = (9/2)arcsin(x/3) - (9/4)(2x√(3² - x²))/9 + C
= (9/2)arcsin(x/3) - (x/2)√(9 - x²) + C