Calculate the antiderivative of (-2x^3+14x^9)/(x^-2)?

Answer 1

∫(-2x^3+14x^9)/(x^-2)dx.......... Start with the given integral


∫(-2x^3)/(x^-2)+(14x^9)/(x^-2).dx......... Break up the fraction


∫(-2x^5)+(14x^11)dx.......... Divide the monomials by subtracting the exponents



∫(-x^6)/3+(14x^12)/12dx.......... Integrate each integral using the power rule



∫(-2x^5)dx+∫(14x^11)dx.......... Break up the integral into two parts



(-2x^6)/6+(14x^12)/12 + C.......... Integrate each integral using the power rule


(-x^6)/3+(7x^12)/6 + C.......... Reduce


(-1/3)x^6+(7/6)x^12 + C.......... Pull out the coefficients

Answer 2

I = ∫ x ² (- 2 x ³ + 14 x^9 ) dx
I = ∫ - 2 x^5 + 14 x^(11) dx
I = (- 2 ) x^6 / 6 + 14 x^(12) / 12 + C
I = (-1/3) x^6 + (7/6) x^(12) + C