2
∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/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.
replace square root o x with t.
∫ f'(x)/(af(x)2 + bf) dx = (1/b)ln[f(x)/(af(x) + b)] + C C is the constant of integration.
square root x
0
2
0
∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/a + C C is the constant of integration.
0
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C C is the constant of integration.
∫ 1/sinh2(x) dx = -cotanh + C C is the constant of integration.
∫ f'(x)/[f(x)√(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.
∫ f'(x)/√(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.
∫ 1/cosh2(x) dx = tanh(x) + C C is the constant of integration.
replace square root o x with t.
∫ f'(x)/(af(x)2 + bf) dx = (1/b)ln[f(x)/(af(x) + b)] + C C is the constant of integration.