跪求两个不定积分,只要最终答案,若能略点明做法更好!题目中“S”代表不定积分符号,“/”代表除以.1.S7sin(8x)cos(5x)dx2.S1/(cosx-1)dx

Question

跪求两个不定积分,只要最终答案,若能略点明做法更好!
题目中“S”代表不定积分符号,“/”代表除以.
1.S 7sin(8x)cos(5x)dx
2.S 1/(cosx-1)dx

Answer 1

1、∫7sin(8x)cos(5x)dx
=7/2*∫[sin(13x)+sin(3x)]dx
=7/2*[-1/13*cos(13x)-1/3*cos(3x)]+c
=-7/78*[3cos(13x)+13cos(3x)]+c
2、∫1/(cosx-1)dx 考虑cosx的倍角公式,将1抵消掉
=∫1/[1-2sin^2 (x/2)-1]dx
=-1/2*∫csc^2 (x/2)dx
=∫dcot(x/2)
=cot(x/2)+c