【數學】幫我檢查一下？

45084503

2, 3 天生病沒去學校ˊˋ
所以自己在課本學東西
幫偶檢查這題ˊˋ


Integrate  ∫(sin x - cos x)(sin x + cos x)5^dx
= u= sin x + cos x
= du= (cos x - sin x)dx = -(sin x - cos x)dx
= (-1)du = (sin x - cos x)dx
= ∫(sin x - cos x)(sin x + cos x)5^dx =  ∫(sin x + cos x)(sin x - cos x)5^dx
= ∫u5^ (-1)du
= (-1) ∫u5^du
= (-1)u6^/6+C
= -(1/6)(sin x + cos x)6^ + C