Did you try to read your post after submitting it?
Use the substitution u = 1 + sinx and intergration to show that
integra (sinxcosx(1+sinx)^5 dx) = (1/42)(1+sinx)^6 [6sinx-1]+C
I have tried ingetrating this by substituion then by parts twice but it still deosnt give me thr answer desired by the question, or maybe my working out is wrong.