为什么∫(π/2,-π/2)sin³xcosxdx=∫(π/2,-π/2)sinxdsinx啊?为什么∫(-π/2,π/2)sin³xcosxdx=∫(-π/2,π/2)sin³xdsinx啊？

为什么∫(π/2,-π/2)sin³xcosxdx=∫(π/2,-π/2)sinxdsinx啊?为什么∫(-π/2,π/2)sin³xcosxdx=∫(-π/2,π/2)sin³xdsinx啊？
为什么∫(π/2,-π/2)sin³xcosxdx=∫(π/2,-π/2)sinxdsinx啊?
为什么∫(-π/2,π/2)sin³xcosxdx=∫(-π/2,π/2)sin³xdsinx啊？

为什么∫(π/2,-π/2)sin³xcosxdx=∫(π/2,-π/2)sinxdsinx啊?为什么∫(-π/2,π/2)sin³xcosxdx=∫(-π/2,π/2)sin³xdsinx啊？
∵(sinx)'=cosx
即dsinx=cosxdx
∴∫(-π/2,π/2)sin³xcosxdx=∫(-π/2,π/2)sin³xdsinx