Integration by Substitution

∫x^3*(x^2+1)^(3/2)*dx=0.5∫x^2*(x^2+1)^(3/2)*d(x^2)=0.5∫x^2*(x^2+1)^1.5*d(x^2+1)=0.5∫(x^2+1-1)*(x^2+1)^1.5*d(x^2+1)=0.5∫[(x^2+1)*(x^2+1)^1.5-(x^2+1)^1.5]*d(x^2+1)=0.5∫[(x^2+1)^2.5-(x^2+1)^1.5]*d(x^2+1)=0.5*[(x^2+1)^3.5/3.5-(x^2+1)^2.5/2.5]+c=(x^2+1)^2.5*[(x^2+1)/7-1/5]+c=(x^2+1)^2.5*[5*(x^2+1)-7]/35+c

2012-12-02 19:05:01 補充：
=(x^2+1)^2.5*[5x^2+5-7]/35+c

=(x^2+1)^2.5*(5x^2-2)/35+c...........ans

圖片參考：http://i1096.photobucket.com/albums/g340/pingshek/2012-12-03-1.png?t=1354466650


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