∫cos√(x+1)d(x+1)
=∫cos√(x+1)d(√(x+1)^2
√(x+1)=t
=∫costdt^2=∫2tcostdt=∫2tdsint=2tsint-2∫sintdt=2tsint+2cost+C
=2√(x+1)sin√(x+1)+2cos√(x+1) +C