Optimal. Leaf size=173 \[ a^4 c x+\frac{1}{2} a^4 d x^2+\frac{1}{3} a^4 e x^3+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+\frac{2}{3} a^3 b e x^6+\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+\frac{2}{3} a^2 b^2 e x^9+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{3} a b^3 e x^{12}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}+\frac{1}{15} b^4 e x^{15} \]
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Rubi [A] time = 0.259694, antiderivative size = 173, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ a^4 c x+\frac{1}{2} a^4 d x^2+\frac{1}{3} a^4 e x^3+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+\frac{2}{3} a^3 b e x^6+\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+\frac{2}{3} a^2 b^2 e x^9+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{3} a b^3 e x^{12}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}+\frac{1}{15} b^4 e x^{15} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x + e*x^2)*(a + b*x^3)^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{4} d \int x\, dx + a^{4} \int c\, dx + a^{3} b c x^{4} + \frac{4 a^{3} b d x^{5}}{5} + \frac{6 a^{2} b^{2} c x^{7}}{7} + \frac{3 a^{2} b^{2} d x^{8}}{4} + \frac{2 a b^{3} c x^{10}}{5} + \frac{4 a b^{3} d x^{11}}{11} + \frac{b^{4} c x^{13}}{13} + \frac{b^{4} d x^{14}}{14} + \frac{e \left (a + b x^{3}\right )^{5}}{15 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x**2+d*x+c)*(b*x**3+a)**4,x)
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Mathematica [A] time = 0.00801525, size = 173, normalized size = 1. \[ a^4 c x+\frac{1}{2} a^4 d x^2+\frac{1}{3} a^4 e x^3+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+\frac{2}{3} a^3 b e x^6+\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+\frac{2}{3} a^2 b^2 e x^9+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{3} a b^3 e x^{12}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}+\frac{1}{15} b^4 e x^{15} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x + e*x^2)*(a + b*x^3)^4,x]
[Out]
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Maple [A] time = 0.002, size = 148, normalized size = 0.9 \[{a}^{4}cx+{\frac{{a}^{4}d{x}^{2}}{2}}+{\frac{{a}^{4}e{x}^{3}}{3}}+{a}^{3}bc{x}^{4}+{\frac{4\,{a}^{3}bd{x}^{5}}{5}}+{\frac{2\,{a}^{3}be{x}^{6}}{3}}+{\frac{6\,{a}^{2}{b}^{2}c{x}^{7}}{7}}+{\frac{3\,{a}^{2}{b}^{2}d{x}^{8}}{4}}+{\frac{2\,{a}^{2}{b}^{2}e{x}^{9}}{3}}+{\frac{2\,a{b}^{3}c{x}^{10}}{5}}+{\frac{4\,a{b}^{3}d{x}^{11}}{11}}+{\frac{a{b}^{3}e{x}^{12}}{3}}+{\frac{{b}^{4}c{x}^{13}}{13}}+{\frac{{b}^{4}d{x}^{14}}{14}}+{\frac{{b}^{4}e{x}^{15}}{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x^2+d*x+c)*(b*x^3+a)^4,x)
[Out]
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Maxima [A] time = 1.41452, size = 198, normalized size = 1.14 \[ \frac{1}{15} \, b^{4} e x^{15} + \frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{1}{3} \, a b^{3} e x^{12} + \frac{4}{11} \, a b^{3} d x^{11} + \frac{2}{5} \, a b^{3} c x^{10} + \frac{2}{3} \, a^{2} b^{2} e x^{9} + \frac{3}{4} \, a^{2} b^{2} d x^{8} + \frac{6}{7} \, a^{2} b^{2} c x^{7} + \frac{2}{3} \, a^{3} b e x^{6} + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{3} \, a^{4} e x^{3} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^4*(e*x^2 + d*x + c),x, algorithm="maxima")
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Fricas [A] time = 0.185243, size = 1, normalized size = 0.01 \[ \frac{1}{15} x^{15} e b^{4} + \frac{1}{14} x^{14} d b^{4} + \frac{1}{13} x^{13} c b^{4} + \frac{1}{3} x^{12} e b^{3} a + \frac{4}{11} x^{11} d b^{3} a + \frac{2}{5} x^{10} c b^{3} a + \frac{2}{3} x^{9} e b^{2} a^{2} + \frac{3}{4} x^{8} d b^{2} a^{2} + \frac{6}{7} x^{7} c b^{2} a^{2} + \frac{2}{3} x^{6} e b a^{3} + \frac{4}{5} x^{5} d b a^{3} + x^{4} c b a^{3} + \frac{1}{3} x^{3} e a^{4} + \frac{1}{2} x^{2} d a^{4} + x c a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^4*(e*x^2 + d*x + c),x, algorithm="fricas")
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Sympy [A] time = 0.088664, size = 178, normalized size = 1.03 \[ a^{4} c x + \frac{a^{4} d x^{2}}{2} + \frac{a^{4} e x^{3}}{3} + a^{3} b c x^{4} + \frac{4 a^{3} b d x^{5}}{5} + \frac{2 a^{3} b e x^{6}}{3} + \frac{6 a^{2} b^{2} c x^{7}}{7} + \frac{3 a^{2} b^{2} d x^{8}}{4} + \frac{2 a^{2} b^{2} e x^{9}}{3} + \frac{2 a b^{3} c x^{10}}{5} + \frac{4 a b^{3} d x^{11}}{11} + \frac{a b^{3} e x^{12}}{3} + \frac{b^{4} c x^{13}}{13} + \frac{b^{4} d x^{14}}{14} + \frac{b^{4} e x^{15}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x**2+d*x+c)*(b*x**3+a)**4,x)
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GIAC/XCAS [A] time = 0.21047, size = 205, normalized size = 1.18 \[ \frac{1}{15} \, b^{4} x^{15} e + \frac{1}{14} \, b^{4} d x^{14} + \frac{1}{13} \, b^{4} c x^{13} + \frac{1}{3} \, a b^{3} x^{12} e + \frac{4}{11} \, a b^{3} d x^{11} + \frac{2}{5} \, a b^{3} c x^{10} + \frac{2}{3} \, a^{2} b^{2} x^{9} e + \frac{3}{4} \, a^{2} b^{2} d x^{8} + \frac{6}{7} \, a^{2} b^{2} c x^{7} + \frac{2}{3} \, a^{3} b x^{6} e + \frac{4}{5} \, a^{3} b d x^{5} + a^{3} b c x^{4} + \frac{1}{3} \, a^{4} x^{3} e + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^4*(e*x^2 + d*x + c),x, algorithm="giac")
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