Math Help - Intergration (Substitution)

1. Intergration (Substitution)

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.

6. Well by defining $u=1+\sin x\implies\frac{du}{dx}=\cos x.$ The rest is a matter of replacement.