Optimal. Leaf size=37 \[ \frac{\left (a+b x+c x^2\right )^{m+1} \left (d+e x+f x^2+g x^3\right )^{n+1}}{x^2} \]
[Out]
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Rubi [F] time = 9.37199, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{\left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5\right )}{x^3},x\right ) \]
Verification is Not applicable to the result.
[In] Int[((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(-2*a*d + (-(b*d) - a*e + b*d*m + a*e*n)*x + (2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 + (c*e + b*f + a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^3 + (2*c*f + 2*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^4 + c*g*(3 + 2*m + 3*n)*x^5))/x^3,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x**2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x**3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x**4+c*g*(3+2*m+3*n)*x**5)/x**3,x)
[Out]
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Mathematica [A] time = 2.20482, size = 34, normalized size = 0.92 \[ \frac{(a+x (b+c x))^{m+1} (d+x (e+x (f+g x)))^{n+1}}{x^2} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(-2*a*d + (-(b*d) - a*e + b*d*m + a*e*n)*x + (2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 + (c*e + b*f + a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^3 + (2*c*f + 2*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^4 + c*g*(3 + 2*m + 3*n)*x^5))/x^3,x]
[Out]
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Maple [A] time = 0.036, size = 38, normalized size = 1. \[{\frac{ \left ( c{x}^{2}+bx+a \right ) ^{1+m} \left ( g{x}^{3}+f{x}^{2}+ex+d \right ) ^{1+n}}{{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x^4+c*g*(3+2*m+3*n)*x^5)/x^3,x)
[Out]
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Maxima [A] time = 0.90355, size = 128, normalized size = 3.46 \[ \frac{{\left (c g x^{5} +{\left (c f + b g\right )} x^{4} +{\left (c e + b f + a g\right )} x^{3} +{\left (c d + b e + a f\right )} x^{2} + a d +{\left (b d + a e\right )} x\right )} e^{\left (n \log \left (g x^{3} + f x^{2} + e x + d\right ) + m \log \left (c x^{2} + b x + a\right )\right )}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*g*(2*m + 3*n + 3)*x^5 + (2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n + 2*c*f + 2*b*g)*x^4 + (2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n + c*e + b*f + a*g)*x^3 + (2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 - 2*a*d + (b*d*m + a*e*n - b*d - a*e)*x)*(g*x^3 + f*x^2 + e*x + d)^n*(c*x^2 + b*x + a)^m/x^3,x, algorithm="maxima")
[Out]
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*g*(2*m + 3*n + 3)*x^5 + (2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n + 2*c*f + 2*b*g)*x^4 + (2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n + c*e + b*f + a*g)*x^3 + (2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 - 2*a*d + (b*d*m + a*e*n - b*d - a*e)*x)*(g*x^3 + f*x^2 + e*x + d)^n*(c*x^2 + b*x + a)^m/x^3,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x**2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x**3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x**4+c*g*(3+2*m+3*n)*x**5)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (c g{\left (2 \, m + 3 \, n + 3\right )} x^{5} +{\left (2 \, c f m + b g m + 2 \, c f n + 3 \, b g n + 2 \, c f + 2 \, b g\right )} x^{4} +{\left (2 \, c e m + b f m + c e n + 2 \, b f n + 3 \, a g n + c e + b f + a g\right )} x^{3} +{\left (2 \, c d m + b e m + b e n + 2 \, a f n\right )} x^{2} - 2 \, a d +{\left (b d m + a e n - b d - a e\right )} x\right )}{\left (g x^{3} + f x^{2} + e x + d\right )}^{n}{\left (c x^{2} + b x + a\right )}^{m}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*g*(2*m + 3*n + 3)*x^5 + (2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n + 2*c*f + 2*b*g)*x^4 + (2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n + c*e + b*f + a*g)*x^3 + (2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 - 2*a*d + (b*d*m + a*e*n - b*d - a*e)*x)*(g*x^3 + f*x^2 + e*x + d)^n*(c*x^2 + b*x + a)^m/x^3,x, algorithm="giac")
[Out]