高等数学 大一需要了解的求导公式 及求不定积分公式

Question

如题所述

Answer 1

1. 求导公式：
- (x^a)' = a*x^(a-1)
- (a^x)' = a^x * ln(a)
- (log_a(x))' = 1 / (x * ln(a))
- (sin(x))' = cos(x)
- (cos(x))' = -sin(x)
- (u*v)' = u'*v + u*v'
- (u+v)' = u' + v'
- (u/v)' = (u'*v - u*v') / v^2
2. 求不定积分公式：
- ∫0*dx = c
- ∫x^u*dx = (x^(u+1))/(u+1) + c
- ∫1/x*dx = ln|x| + c
- ∫a^x*dx = (a^x) / ln(a) + c
- ∫e^x*dx = e^x + c
- ∫sin(x)*dx = -cos(x) + c
- ∫cos(x)*dx = sin(x) + c
- ∫1/(cos(x))^2*dx = tan(x) + c
- ∫1/(sin(x))^2*dx = -cot(x) + c
- ∫1/√(1-x^2)*dx = arcsin(x) + c
- ∫1/(1+x^2)*dx = arctan(x) + c
- ∫1/(a^2-x^2)*dx = (1/(2*a)) * ln|(a+x)/(a-x)| + c
- ∫sec(x)*dx = ln|sec(x) + tan(x)| + c
- ∫1/(a^2+x^2)*dx = 1/a * arctan(x/a) + c
- ∫1/√(a^2-x^2)*dx = arcsin(x/a) + c
- ∫sec^2(x)*dx = tan(x) + c
- ∫sinh(x)*dx = cosh(x) + c
- ∫cosh(x)*dx = sinh(x) + c
- ∫tanh(x)*dx = ln|cosh(x)| + c