分部积分问题:x^2 * tanx dx最好能用mathtype截图发上来,这样更容易理解3x^3tanx - 1/3∫x^3 d(tanx)=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx这一步哪来的?
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![分部积分问题:x^2 * tanx dx最好能用mathtype截图发上来,这样更容易理解3x^3tanx - 1/3∫x^3 d(tanx)=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx这一步哪来的?](/uploads/image/z/8715387-3-7.jpg?t=%E5%88%86%E9%83%A8%E7%A7%AF%E5%88%86%E9%97%AE%E9%A2%98%EF%BC%9Ax%5E2+%2A+tanx+dx%E6%9C%80%E5%A5%BD%E8%83%BD%E7%94%A8mathtype%E6%88%AA%E5%9B%BE%E5%8F%91%E4%B8%8A%E6%9D%A5%2C%E8%BF%99%E6%A0%B7%E6%9B%B4%E5%AE%B9%E6%98%93%E7%90%86%E8%A7%A33x%5E3tanx+-+1%2F3%E2%88%ABx%5E3+d%28tanx%29%3D1%2F3x%5E3tanx+-+1%2F3%E2%88%ABx%5E3%2F%28x%5E2%2B1%29+dx%E8%BF%99%E4%B8%80%E6%AD%A5%E5%93%AA%E6%9D%A5%E7%9A%84%EF%BC%9F)
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分部积分问题:x^2 * tanx dx最好能用mathtype截图发上来,这样更容易理解3x^3tanx - 1/3∫x^3 d(tanx)=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx这一步哪来的?
分部积分问题:x^2 * tanx dx
最好能用mathtype截图发上来,这样更容易理解
3x^3tanx - 1/3∫x^3 d(tanx)
=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx
这一步哪来的?
分部积分问题:x^2 * tanx dx最好能用mathtype截图发上来,这样更容易理解3x^3tanx - 1/3∫x^3 d(tanx)=1/3x^3tanx - 1/3∫x^3/(x^2+1) dx这一步哪来的?
答:
原积分
=∫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
因为d(tanx)=1/(1+x^2) dx
(tanx)'=1/(1+x^2)