不定积分 练习 (1)∫(tanx)2sec2xdx (2)∫(cotx)2csc2xdx (tanx)3 +C =(co)C 3 3
(�𝒏𝒂𝒕�) (1( 𝟐 𝐬𝒆𝒄 (�𝒕𝒐𝒄�) (2𝟐𝒙𝒅𝒙 ( 𝟐𝒄𝒔𝒄 𝟐𝒙𝒅𝒙 练习 = (𝒕𝒂𝒏𝒙) 𝟑 𝟑 + 𝑪 = − (𝒄𝒐𝒕𝒙) 𝟑 𝟑 + 𝑪
不定积分 3) arcsinx dx (4∫ rctanx √1-x2 1+x2 dx 解-Jaresinx dx =∫arctanx'dx 解 =∫arcsinx·darcsinx =∫arctanx·darctanx =∫udu u arcsinx =∫udu u arctanx u2 +C F+c 2
(3( 𝒂𝒓𝒄𝒔𝒊𝒏𝒙 𝟏−𝒙 𝟐 (4𝒅𝒙 ( 𝒂𝒓𝒄𝒕𝒂𝒏𝒙 𝟏+𝒙 𝟐 𝒅𝒙 解: �𝒏𝒊𝒔𝒄𝒓𝒂𝒅� ∙ �𝒏𝒊𝒔𝒄𝒓𝒂� = �𝒏𝒊𝒔𝒄𝒓𝒂� = �� �𝒅𝒖� = = 𝒖 𝟐 𝟐 + 𝑪 ∙ �𝒏𝒂𝒕𝒄𝒓𝒂� = :解 𝟏 𝟏+𝒙 𝟐 𝒅𝒙 �𝒏𝒂𝒕𝒄𝒓𝒂𝒅� ∙ �𝒏𝒂𝒕𝒄𝒓𝒂� = �𝒏𝒂𝒕𝒄𝒓𝒂� = �� �𝒅𝒖� = = (𝒂𝒓𝒄𝒔𝒊𝒏𝒙) 𝟐 𝟐 + 𝑪 = (𝒂𝒓𝒄𝒕𝒂𝒏𝒙) 𝟐 𝟐 + 𝑪 ∙ �𝒏𝒊𝒔𝒄𝒓𝒂� = 𝟏 𝟏−𝒙 𝟐 𝒅𝒙 = 𝒖 𝟐 𝟐 + 𝑪