∫  2x12+5x9dx1+x3+x53=

I=∫  2x12+5x91+x3+x53dx=∫  5x−6+2x−3dx1+x−2+x−53 Putting 1+x-2+x-5=t , then       −2x−3−5x−6dx=dt∴           I=−∫  dtt3=12t2=121+x−2+x−52        =x102x5+x3+12+c