∫ f'(x)/[f(x)√(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C
C is the constant of integration.
the total product divided by quantity
10
25
4 divided by (n5)
-(x-1)-1 or -1/(x-1)
∫ f'(x)/√(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C C is the constant of integration.
∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/a + C C is the constant of integration.
2
∫ f'(x)/f(x) dx = ln(f(x)) + C C is the constant of integration.
0
0
∫ [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C C is the constant of integration.
∫ f'(x)/(af(x)2 + bf) dx = (1/b)ln[f(x)/(af(x) + b)] + C C is the constant of integration.
2
0
∫ f(x)/(1 - f(x)) dx = -x + ∫ 1/(1 - f(x)) dx