∫dx/√(3+4x)
=(1/4)∫d(3+4x)/√(3+4x)
=(1/4)∫(3+4x)^(-1/2)d(3+4x)
=(1/4)*2*(3+4x)^(1/2)+C
=(1/2)*(3+4x)^(1/2)+C