不定积分的典型例题
例1．計算?Skip Record If...?
解法1
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而?Skip Record If...??Skip Record If...?所以
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解法2 ?Skip Record If...?
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解法3
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由拼接法可有
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例2.求?Skip Record If...?
解将被积函数化为简单的部分分式
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两边同乘以?Skip Record If...?，约去?Skip Record If...?的因子后令?Skip Record If...?得?Skip Record If...?
两边同乘以?Skip Record If...?，对?Skip Record If...?求导，再令?Skip Record If...?，施以上运算后，右端得A,而左端为
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在分解式（*）中令?Skip Record If...?得?Skip Record If...?所以?Skip Record If...?分解式（*）两边同乘以?Skip Record If...?，再令?Skip Record If...?得?Skip Record If...?故有
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例3.求?Skip Record If...?
解令?Skip Record If...?再用部分分式，則
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?Skip Record If...?两边乘以?Skip Record If...?再令?Skip Record If...?得?Skip Record If...?两边乘以?Skip Record If...?再令?Skip Record If...?得?Skip Record If...?两边乘以
?Skip Record If...?再令?Skip Record If...?得?Skip Record If...?令?Skip Record If...?
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例4 ?Skip Record If...?
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If...?
例5.求?Skip Record If...?
解令?Skip Record If...?则?Skip Record If...?
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例6 ?Skip Record If...?
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?Skip Record If...?例7
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例8
?Skip Record If...??Skip Record If...?例9．
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例10．
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例 11
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例12．求?Skip Record If...?其中?Skip Record If...?
解由配方得
?Skip Record If...?，令?Skip Record If...?则有原式
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例13．求?Skip Record If...?
解?Skip Record If...?
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?Skip Record If...?解上面的联立方程可得出
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例14．计算?Skip Record If...?
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例15．?Skip Record If...?
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例16．求?Skip Record If...?
解令
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例17．设?Skip Record If...?有一个原函数?Skip Record If...?求?Skip Record If...?
解用分部积分法有
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代入（*）有
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即?Skip Record If...?
例18．求?Skip Record If...?
解?Skip Record If...?被积函数的分子是?Skip Record If...?的线性组合，故有
?Skip Record If...?于是
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例19．求?Skip Record If...?
解?Skip Record If...?
?Skip Record If...?例20．?Skip Record If...?
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例21．
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例22．
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例23．
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例24．
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例25．?Skip Record If...?
例26．?Skip Record If...?
例27．?Skip Record If...?
例28．
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例29.?Skip Record If...?
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例30.
?Skip Record If...?例31
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例32.
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例33.
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例34．
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例35．?Skip Record If...?
例36．?Skip Record If...?
例37
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例38．
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例39．
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例40．
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例41．
?Skip Record If...?例42．
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例43．
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例44．?Skip Record If...?（令?Skip Record If...?）
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例45．?Skip Record If...?（先约分，分子加一减一）
例46．?Skip Record If...?
例47．
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例48．
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例49．?Skip Record If...?
例50．
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例51．?Skip Record If...?
（分项分部积分）?Skip Record If...?
例52．求?Skip Record If...?
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例53．求?Skip Record If...?
解令?Skip Record If...?
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利用原函数的连续性，有
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从而解出?Skip Record If...?
故?Skip Record If...?