Optimal. Leaf size=34 \[ \left (a+b x+c x^2\right )^{m+1} \left (d+e x+f x^2+g x^3\right )^{n+1} \]
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Rubi [A] time = 0.12, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 164, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {1590} \begin {gather*} \left (a+b x+c x^2\right )^{m+1} \left (d+e x+f x^2+g x^3\right )^{n+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 1590
Rubi steps
\begin {align*} \int \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4\right ) \, dx &=\left (a+b x+c x^2\right )^{1+m} \left (d+e x+f x^2+g x^3\right )^{1+n}\\ \end {align*}
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Mathematica [A] time = 0.31, size = 31, normalized size = 0.91 \begin {gather*} (a+x (b+c x))^{m+1} (d+x (e+x (f+g x)))^{n+1} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 1.24, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 35, normalized size = 1.03 \begin {gather*} \left (c \,x^{2}+b x +a \right )^{m +1} \left (g \,x^{3}+f \,x^{2}+e x +d \right )^{n +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.70, size = 92, normalized size = 2.71 \begin {gather*} {\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 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.78, size = 148, normalized size = 4.35 \begin {gather*} {\left (g\,x^3+f\,x^2+e\,x+d\right )}^n\,\left (x^4\,\left (b\,g+c\,f\right )\,{\left (c\,x^2+b\,x+a\right )}^m+x^2\,{\left (c\,x^2+b\,x+a\right )}^m\,\left (a\,f+b\,e+c\,d\right )+x^3\,{\left (c\,x^2+b\,x+a\right )}^m\,\left (a\,g+b\,f+c\,e\right )+a\,d\,{\left (c\,x^2+b\,x+a\right )}^m+x\,\left (a\,e+b\,d\right )\,{\left (c\,x^2+b\,x+a\right )}^m+c\,g\,x^5\,{\left (c\,x^2+b\,x+a\right )}^m\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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