Evaluate the indefinite integral? Integral [(cosx)/(4sinx+20)]dx

Note that if you make a substitute u = 4*sin(x) + 20, du/4 = cos(x) dx and your integral transforms into:

1/4*∫du/u = 1/4*ln|u| + C = 1/4*ln|4*sin(x) + 20| + C