Question

求不定积分的过程，图上有答案

Answer 1

1. ∫(cosx)^3 * dx

   =∫(cosx)^2 * (cosx * dx)

   =∫[1 - (sinx)^2] * d(sinx)        注：d(sinx) = cosx * dx

   =∫d(sinx) - ∫(sinx)^2 * d(sinx)

   =sinx - 1/3 * (sinx)^3 + C

2. ∫dx/(sinx * cosx)

   =∫dx/[(sinx/cosx) * (cosx)^2]           

   =∫(1/cosx)^2 * dx/(tanx)                   注：tanx = sinx /cosx

   =∫(secx)^2 * dx /(tanx)                     注：(secx) = 1/cosx

   =d(tanx) /(tanx)                              注：d(tanx) = (secx)^2 * dx

   =ln|tanx| + C

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谢谢