高数不定积分问题求解,
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高数不定积分问题求解,
请给出详细解答过程以及解决这类题型的诀窍(如果有的话),
![](http://img.wesiedu.com/upload/f/02/f021d1dedf0745acccce8fb203087cdb.jpg)
请给出详细解答过程以及解决这类题型的诀窍(如果有的话),
![](http://img.wesiedu.com/upload/f/02/f021d1dedf0745acccce8fb203087cdb.jpg)
![高数不定积分问题求解,](/uploads/image/z/15115771-19-1.jpg?t=%E9%AB%98%E6%95%B0%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E9%97%AE%E9%A2%98%E6%B1%82%E8%A7%A3%2C)
设(x-1)/(x+1)=t³,则dx=6t²dt/(1-t³)²,x+1=2/(1-t³),x-1=2t³/(1-t³)
∴原式=∫[6t²dt/(1-t³)²]/{[2/(1-t³)]^(2/3)*[2t³/(1-t³)]^(4/3)}
=∫(6t²dt)/[2²t^4]
=3/2∫dt/t²
=(-3/2)/t+C
=(-3/2)[(x+1)/(x-1)]^(1/3)+C (C是积分常数)
或者
![](http://img.wesiedu.com/upload/e/2f/e2fa1453a87227fc8b9cfa4cd3cf3d3b.jpg)
∴原式=∫[6t²dt/(1-t³)²]/{[2/(1-t³)]^(2/3)*[2t³/(1-t³)]^(4/3)}
=∫(6t²dt)/[2²t^4]
=3/2∫dt/t²
=(-3/2)/t+C
=(-3/2)[(x+1)/(x-1)]^(1/3)+C (C是积分常数)
或者
![](http://img.wesiedu.com/upload/e/2f/e2fa1453a87227fc8b9cfa4cd3cf3d3b.jpg)