X2+9的平方之一的不定积分

x = 3tanθ、dx = 3sec^2(θ) dθ∫ dx/(x^2 + 9)^2= ∫ [3sec^2(θ)]/[9sec^2(θ)]^2 dθ= ∫ [3sec^2(θ)]/[81sec^4(θ)] dθ= (1/27)∫ cos^2(θ) dθ= (1/54)∫ (1 + cos2θ) dθ= (1/54)θ + (1/108)sin2θ + C...