求不定积分∫√x/（x^4/3+1）dx
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∫√xdx/(x^(3/4)+1)
=(2/3)∫dx^(3/2)/(1+x^(3/4))
=(4/3)∫x^(3/4)dx^(3/4) /(1+x^(3/4))
=(4/3)x^(3/4)-(4/3)ln|1+x^(3/4)|+C
∫√xdx/(x^(4/3)+1)
=(2/3)∫dx^(3/2)/(1+x^(4/3))
=(2/3)∫9x^(8/6)d(x^(1/6)/(1+x^(4/3))
=6∫x^(4/3)dx^(1/6)/(1+x^(4/3))
=6x^(1/6)-6∫dx^(1/6)/(1+x^(8/6))
无法用初等函数表示
x^(1/6)=t ∫dx^(1/6)/(1+x^(8/6))=∫dt/(1+t^8)无法用初等函数表示
=(2/3)∫dx^(3/2)/(1+x^(3/4))
=(4/3)∫x^(3/4)dx^(3/4) /(1+x^(3/4))
=(4/3)x^(3/4)-(4/3)ln|1+x^(3/4)|+C
∫√xdx/(x^(4/3)+1)
=(2/3)∫dx^(3/2)/(1+x^(4/3))
=(2/3)∫9x^(8/6)d(x^(1/6)/(1+x^(4/3))
=6∫x^(4/3)dx^(1/6)/(1+x^(4/3))
=6x^(1/6)-6∫dx^(1/6)/(1+x^(8/6))
无法用初等函数表示
x^(1/6)=t ∫dx^(1/6)/(1+x^(8/6))=∫dt/(1+t^8)无法用初等函数表示
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