1/( x^1/2+x^1/4)的不定积分

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1/(x^1/2+x^1/4)的不定积分1/(x^1/2+x^1/4)的不定积分 1/(x^1/2+x^1/4)的不定积分45令x^(1/4)=u,则x=u^4,dx=4u^3du∫dx/[

1/( x^1/2+x^1/4)的不定积分
1/( x^1/2+x^1/4)的不定积分
 

1/( x^1/2+x^1/4)的不定积分
45 令 x^(1/4)=u,则 x=u^4,dx=4u^3du
∫dx/[x^(1/2)+x^(1/4)] = ∫4u^3du/[u^2+u]
= 4∫[u-1+1/(u+1)]du = 2u^2-4u+4ln|u+1|+C
= 2x^(1/2)-4x^(1/4)+4ln[x^(1/4)+1]+C