不定积分1/根号x+立方根下x^2

Question

不定积分 1/根号x+立方根下x^2

Answer 1

用换元法,令六次根号x=t
则x=t^6
根号x=t^3,立方根下x^2=t^4
dx=6t^5dt
原式
=∫1/(t^3+t^4)*6t^5dt
=6∫t^2/(1+t)dt
=6∫(t^2-1+1)/(1+t)dt
=6∫[(t-1)+1/(1+t)]dt
=3t^2+6t+6ln(1+t)+C
反代吧