求解不定积分!!!!
2个回答
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你好!可以采用分部积分法,具体如下:
∫x^2 tanx dx
=∫1/3*tanx d(x^3)=1/3x^3tanx - 1/3∫x^3 d(tanx)=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx=1/3x^3tanx - 1/3∫(x^3+x-x)/(x^2+1) dx=1/3x^3tanx - 1/3∫x-x/(x^2+1) dx=1/3x^3tanx - 1/3∫x dx + 1/3∫x/(x^2+1) dx=1/3x^3tanx - 1/6x^2 + 1/3∫x/(x^2+1) dx=1/3x^3tanx - 1/6x^2 + 1/3∫1/2*1/(x^2+1) d(x^2+1)=1/3x^3tanx - 1/6x^2 + 1/6ln(x^2+1) + C
满意请采纳,谢谢~
∫x^2 tanx dx
=∫1/3*tanx d(x^3)=1/3x^3tanx - 1/3∫x^3 d(tanx)=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx=1/3x^3tanx - 1/3∫(x^3+x-x)/(x^2+1) dx=1/3x^3tanx - 1/3∫x-x/(x^2+1) dx=1/3x^3tanx - 1/3∫x dx + 1/3∫x/(x^2+1) dx=1/3x^3tanx - 1/6x^2 + 1/3∫x/(x^2+1) dx=1/3x^3tanx - 1/6x^2 + 1/3∫1/2*1/(x^2+1) d(x^2+1)=1/3x^3tanx - 1/6x^2 + 1/6ln(x^2+1) + C
满意请采纳,谢谢~
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你做的是错的啊
dtanx不是1/1+x^2
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