How does ∫ sin(x)/cos(x)dx become sin(x)+C? Why did cos(x) disapear?
2 answers
it is ∫ cos(x)/sin(x)dx not ∫ sin(x)/cos(x)dx.
Substitution: sin ( x ) = u , cos ( x ) dx = du
∫ cos ( x ) dx / sin ( x ) = ∫ du / u = ln | ( u ) | + C = ln | sin ( x ) | + C
∫ cos ( x ) dx / sin ( x ) = ∫ du / u = ln | ( u ) | + C = ln | sin ( x ) | + C
9 answers