用换元法计算不定积分
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用换元法计算不定积分
用换元法计算不定积分
用换元法计算不定积分
令t=x^(1/4)
原积分=∫1/[t^2*(1+t)]*d(t^4)
=∫4*t^3/[t^2*(1+t)]*dt
=∫4t/(1+t)*dt
=∫(4t+4-4)/(1+t)*dt
=∫4*dt - ∫4/(1+t)*d(t+1)
=4t-4ln(1+t)+c
=4x^(1/4)-4ln[1+x^(1/4)]+c