几道不定积分

Question

如图拜托啦

Answer 1

∫xsinxdx =-∫xd(cosx) =-(xcosx-∫cosxdx) =-(xcosx-sinx)+C =sinx-xcosx+C 令lnx=t，则x=e^t ∫lnx dx =∫td(e^t) =∫t·e^t dt =(t-1)·e^t +C =xlnx -x +C 令arcsinx=t，则x=sint ∫arcsinxdx =∫td(sint) =tsint-∫sintdt =tsint+cost+C =x·arcsinx+cos(arcsinx)+C =x·arcsinx+√(1-x2)+C追问

能否写在纸上

Answer 2

∫dx/sinx = ∫cscxdx = ln|cscx-cotx| + C
∫dx/cosx = ∫secxdx = ln|secx+tanx| + C
∫dx/(sinx)^2 = ∫(cscx)^2dx = -cotx + C
∫dx/(cosx)^2 = ∫(secx)^2dx = tanx + C
∫ f(1/√x)dx = x^2 + C, f(1/√x) = 2x = 2/(1/√x)^2,
f(u) = 2/u^2, ∫ f(x)dx = ∫2dx/x^2 = -2/x + C本回答被网友采纳