Separate the integrals.
f(x) = int3sinxdx - intxcosxdx
Integrate intxcosxdx by parts. Let u = x and dv= cosxdx. Then du = dx and v= sinx.
intudv = uv - intvdu
intxcosx = xsinx - intsinxdx
intxcosx = xsinx - (-cosx) + C
intxcosx = xsinx + cosx + C
Put this together:
f(x) = int3sinxdx - (xsinx + cosx) + C
f(x) = int3sinxdx - xsinx - cosx + C
f(x) = C - 3cosx - xsinx - cosx
You can solve for C now. We know that when x= (7pi)/8, y = 0.
0 = C - 3cos((7pi)/8) - (7pi)/8sin((7pi)/8) - cos((7pi)/8)
C = 3cos((7pi)/8) + (7pi)/8sin((7pi)/8) + cos((7pi)/8)
This will not be an exact expression. An approximation using a calculator yields C ~~ -2.64.
Therefore, f(x) = -cosx - xsinx - 3cosx - 2.64.
Hopefully this helps!