zhuxinfeng
幼苗
共回答了19个问题采纳率:68.4% 举报
都是很基础的题目,不明再问.
(2)
∫ sin(t/4) dt
= 4∫ sin(t/4) d(t/4)
= - 4cos(t/4) + C
(3)
∫ (x² - 3x + 7)(2x - 3) dx
= ∫ (x² - 3x + 7) d(x² - 3x)
= ∫ (x² - 3x + 7) d(x² - 3x + 7)
= (1/2)(x² - 3x + 7) + C
(8)
∫ √(e^x - 2) e^x dx
= ∫ √(e^x - 2) d(e^x)
= ∫ √(e^x - 2) d(e^x - 2)
= (2/3)(e^x - 2)^(3/2) + C
(9)
∫ 2/(xln²x) dx
= 2∫ 1/ln²x d(lnx)
= - 2/lnx + C
(11)
∫ 1/(5 - 2x) dx
= (- 1/2)∫ 1/(5 - 2x) d(- 2x)
= (- 1/2)∫ 1/(5 - 2x) d(5 - 2x)
= (- 1/2)ln|5 - 2x| + C
(13)
∫ sinx/(a - bcosx) dx
= ∫ 1/(a - bcosx) d(- cosx)
= (1/b)∫ 1/(a - bcosx) d(- bcosx)
= (1/b)∫ 1/(a - bcosx) d(a - bcosx)
= (1/b)ln|a - bcosx| + C
(14)
∫ 2x³sinx⁴ dx
= 2∫ sinx⁴ d(x⁴/4)
= (- 1/8)cosx⁴ + C
公式:
∫ x^n dx = x^(n + 1)/(n + 1) + C
∫ sinx dx = - cosx + C
∫ sin(kx) = (- 1/k)cos(kx) + C
∫ 1/(a + bx) dx = (1/b)ln|a + bx| + C
其中凑微分法是很常用的:
∫ ƒ[g(x)] * g'(x) dx = ∫ ƒ[g(x)] d[g(x)] = F[g(x)] + C,F(x)为ƒ(x)的原函数
1年前
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