Simplify the integrand for x>0: x30+x25=x25(x5+1), so its fifth root is x5(x5+1)1/5. Thus the integrand equals 1/[x5(x5+1)1/5]=x−6(1+x−5)−1/5. Since d/dx(1+x−5)=−5x−6, an antiderivative is −(1/4)(1+x−5)4/5. At x=242−1/5, x−5=242, so the value is −(1/4)(243)4/5=−(1/4)(34)=−81/4. At x=31−1/5, x−5=31, so the value is −(1/4)(32)4/5=−(1/4)(24)=−4. Therefore the integral is (−81/4)−(−4)=(−81+16)/4=−65/4. The correct option is −65/4.