Integrate $fracx^2-4x+10x^2sqrt x$
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite Find the indefinate integral with respect to $x$ of $$fracx^2-4x+10x^2sqrt x$$ For this problem I first made each individual number in the numerator separate from each other for easier integration and then simplified $$=int left(fracx^2x^2sqrt x-frac4xx^2sqrt x+frac10x^2sqrt xright)dx$$ $$=int left(x^2x^-frac32-4x^1x^-frac32+10x^-frac32right)dx$$ $$=int left(x^frac12-4x^-frac12+10x^-frac32right)dx$$ I then integrated the expression to get $$frac2x^frac323-8x^frac12-20x^-frac12$$ This is, however, wrong. Any ideas as to why? Thanks in advance $:)$ calculus integration algebra-precalculus share | cite | improve this question edited Aug 31 at 12:15 greedoid 28k 9 37 76 asked Aug 31 at 8:03 Pablo 336 12 3 Note that $x^2sqrtx=x^2+frac12=x^frac52$. – Robert Z Aug 31 at 8:09 1 The powers in the integrand are $-1/2,-3/2,-5/2$. ...