不定积分的凑微分换元积分法举例1：
f ( x ) = ∫ x 2 e x 3 d x = ∫ e x 3 x 2 d x = ∫ e x 3 ( x 2 d x ) = ∫ e x 3 d ( x 3 3 ) = ∫ e t d ( t 3 ) = 1 3 ∫ e t d t = 1 3 ( e t + C ) = 1 3 e t + 1 3 C = 1 3 e t + C = 1 3 e x 3 + C f(x) = int x^2 e^{x^3} dx \ = int e^{x^3} x^2 dx \ = int e^{x^3} (x^2 dx) \ = int e^{x^3} d( frac {x^3} 3) \ = int e^{t} d( frac t 3) \ = frac 1 3 int e^{t} dt \ = frac 1 3 (e^t+C) \ = frac 1 3 e^t+frac 1 3 C \ = frac 1 3 e^t+C \ = frac 1 3 e^{x^3}+C \ f(x)=∫x2ex3dx =∫ex3x2dx =∫ex3(x2dx) =∫ex3d(3x3) =∫etd(3t) =31∫etdt =31(et+C) =31et+31C =31et+C =31ex3+傲娇的荔枝/p>
附KaTex代码：
$$f(x) = int x^2 e^{x^3} dx \ = int e^{x^3} x^2 dx \ = int e^{x^3} (x^2 dx) \ = int e^{x^3} d( frac {x^3} 3) \ = int e^{t} d( frac t 3) \ = frac 1 3 int e^{t} dt \ = frac 1 3 (e^t+C) \ = frac 1 3 e^t+frac 1 3 C \ = frac 1 3 e^t+C \ = frac 1 3 e^{x^3}+C \$$