不定积分∫sin （3-5x） dx

网友回答

-cos(3-5x)+C
======以下答案可供参考======
供参考答案1:
F =cos(3 - 5*x)/5+C
供参考答案2:
Method 1 ：换元积分法
令u = 3-5x，du = -5dx -> dx = (-1/5)du
原式 = ∫ sinu * (-1/5)du
= (-1/5) * (-cosu) + c
= (1/5)cos(3-5x) + c
Method 2：凑微分法
∫ sin(3-5x) dx
= ∫ sin(3-5x) d(-5x) / (-5)，先凑个-5，乘以-5再除以-5
= (-1/5)∫ sin(3-5x) d(-5x)
= (-1/5)∫ sin(3-5x) d(-5x+3)，再凑个+3
= (-1/5)∫ sin(3-5x) d(3-5x)
= (-1/5) * [-cos(3-5x)] + c
= (1/5)cos(3-5x) + c