∫ √x/(√x- 3^√x) dx
换元,x=t^6
=∫ t^3 / (t^3-t^2) d(t^6)
=∫ t^3(6t^5) / (t^3-t^2) dt
=6∫ t^6/(t-1) dt
=6∫ (t^6-1+1)/(t-1) dt
=6∫ (t^5+t^4+t^3+t^2+t+1) dt + 6∫ 1/(t-1) d(t-1)
=6(t^6/6+t^5/5+t^4/4+t^3/3+t^2/2+t)+6ln|t-1|+C
=t^6+6t^5/5+3t^4/2+2t^3+3t^2+6t+6ln|t-1|+C
=x+6x^(5/6)/5+3x^(2/3)/2+2x^(1/2)+3x^(1/3)+6x^(1/6)+6ln|x^(1/6)-1|+C
有不懂欢迎追问
猜你喜欢
- 1从2000这个数减去254以后,再加上245,然后再减去254,再加上245.这样一直下去,当减第《 》次时,得数恰好第一次等于0
- 2I will never see him again和I would never see him again的区别?
- 3若把甲烷分子中的一个氢原子换成氯原子,还是正四面体结构么
- 4多得那么轻易——是病句吗?
- 5已知tanα=3,则2/3sin^2α+4cos^α=
- 6我敬佩的一个人作文600字(最好是写老师的)
- 7下列正确的是:A金属单质都有毒B金属单质都能导电(说明理由)
- 8The cloth is made ( ) cotton.方空中应该填of还是from?
- 9What season do you like?3.Where were you during the summer holiday 如何回答
- 10设tan=2 求1+2sinacosa/sin平方a-cos平方a