谁能帮忙解高等数学题,多谢

发布网友发布时间：2024-03-07 22:13

共1个回答

热心网友时间：2024-06-01 12:48

1.∫(3-2x)³dx = -1/2 *∫(3-2x)³d(3-2x) = -[(3-2x)^4]/8 + C

2.令t³ = 2-3x,则dx = -t²dt
∫dx/(2-3x)^(1/3) = ∫-t²dt/t = -t²/2 + C = -(2-3x)^(2/3)/2 + C

3.令x² = t,则dt = 2xdx
∫sin√t/√t dt = ∫sinx/x 2xdx = -2cosx + C = -2cos√t + C

4.令x = sect,则dx = sect tantdt
∫dx/x√(x²-1) = ∫sect tantdt/(sect tant) = t + C = arccos(1/x) + C

5.令x = tant,则dx = sec²tdt
∫dx/(x²+1)^(3/2) = ∫sec²tdt/sec³t = ∫costdt = sint + C = x/√(x²+1) + C

6.令x = 3sect,则dx = 3sect tantdt
∫√(x²-9)dx/x = ∫3tant 3sect tantdt/3sect = ∫3tan²tdt = ∫(3sec²t-3)dt = 3tant - 3t + C = √(x²-9) - 3arccos(3/x) + C

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