∫(x+1)/(x^2+1) dx ∫上限x^3-1,下线0,f(t)dt=x,求f(7)
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∫(x+1)/(x^2+1) dx ∫上限x^3-1,下线0,f(t)dt=x,求f(7)
∫(x+1)/(x^2+1) dx ∫上限x^3-1,下线0,f(t)dt=x,求f(7)
∫(x+1)/(x^2+1) dx ∫上限x^3-1,下线0,f(t)dt=x,求f(7)
两题,没有关系吧?
∫ (x + 1)/(x² + 1) dx
= ∫ x/(x² + 1) dx + ∫ 1/(1 + x²) dx
= (1/2)ln(1 + x²) + arctan(x) + C
∫(0→x³ - 1) f(t) dt = x,两边,对x求导
(x³ - 1)' * f(x³ - 1) = 1
3x²f(x³ - 1) = 1
f(x³ - 1) = 1/(3x²)
令x = 2,得
f(8 - 1) = 1/(3 * 4) = 1/12
即f(7) = 1/12