Optimal. Leaf size=81 \[ \frac{a^4 (a+b x)^{11}}{11 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{6 a^2 (a+b x)^{13}}{13 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5} \]
[Out]
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Rubi [A] time = 0.100929, antiderivative size = 81, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^4 (a+b x)^{11}}{11 b^5}-\frac{a^3 (a+b x)^{12}}{3 b^5}+\frac{6 a^2 (a+b x)^{13}}{13 b^5}+\frac{(a+b x)^{15}}{15 b^5}-\frac{2 a (a+b x)^{14}}{7 b^5} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x)^10,x]
[Out]
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Rubi in Sympy [A] time = 21.842, size = 73, normalized size = 0.9 \[ \frac{a^{4} \left (a + b x\right )^{11}}{11 b^{5}} - \frac{a^{3} \left (a + b x\right )^{12}}{3 b^{5}} + \frac{6 a^{2} \left (a + b x\right )^{13}}{13 b^{5}} - \frac{2 a \left (a + b x\right )^{14}}{7 b^{5}} + \frac{\left (a + b x\right )^{15}}{15 b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x+a)**10,x)
[Out]
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Mathematica [A] time = 0.0041105, size = 130, normalized size = 1.6 \[ \frac{a^{10} x^5}{5}+\frac{5}{3} a^9 b x^6+\frac{45}{7} a^8 b^2 x^7+15 a^7 b^3 x^8+\frac{70}{3} a^6 b^4 x^9+\frac{126}{5} a^5 b^5 x^{10}+\frac{210}{11} a^4 b^6 x^{11}+10 a^3 b^7 x^{12}+\frac{45}{13} a^2 b^8 x^{13}+\frac{5}{7} a b^9 x^{14}+\frac{b^{10} x^{15}}{15} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x)^10,x]
[Out]
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Maple [A] time = 0.003, size = 113, normalized size = 1.4 \[{\frac{{b}^{10}{x}^{15}}{15}}+{\frac{5\,a{b}^{9}{x}^{14}}{7}}+{\frac{45\,{a}^{2}{b}^{8}{x}^{13}}{13}}+10\,{a}^{3}{b}^{7}{x}^{12}+{\frac{210\,{a}^{4}{b}^{6}{x}^{11}}{11}}+{\frac{126\,{a}^{5}{b}^{5}{x}^{10}}{5}}+{\frac{70\,{a}^{6}{b}^{4}{x}^{9}}{3}}+15\,{a}^{7}{b}^{3}{x}^{8}+{\frac{45\,{a}^{8}{b}^{2}{x}^{7}}{7}}+{\frac{5\,{a}^{9}b{x}^{6}}{3}}+{\frac{{a}^{10}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x+a)^10,x)
[Out]
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Maxima [A] time = 1.3267, size = 151, normalized size = 1.86 \[ \frac{1}{15} \, b^{10} x^{15} + \frac{5}{7} \, a b^{9} x^{14} + \frac{45}{13} \, a^{2} b^{8} x^{13} + 10 \, a^{3} b^{7} x^{12} + \frac{210}{11} \, a^{4} b^{6} x^{11} + \frac{126}{5} \, a^{5} b^{5} x^{10} + \frac{70}{3} \, a^{6} b^{4} x^{9} + 15 \, a^{7} b^{3} x^{8} + \frac{45}{7} \, a^{8} b^{2} x^{7} + \frac{5}{3} \, a^{9} b x^{6} + \frac{1}{5} \, a^{10} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.186029, size = 1, normalized size = 0.01 \[ \frac{1}{15} x^{15} b^{10} + \frac{5}{7} x^{14} b^{9} a + \frac{45}{13} x^{13} b^{8} a^{2} + 10 x^{12} b^{7} a^{3} + \frac{210}{11} x^{11} b^{6} a^{4} + \frac{126}{5} x^{10} b^{5} a^{5} + \frac{70}{3} x^{9} b^{4} a^{6} + 15 x^{8} b^{3} a^{7} + \frac{45}{7} x^{7} b^{2} a^{8} + \frac{5}{3} x^{6} b a^{9} + \frac{1}{5} x^{5} a^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.169596, size = 131, normalized size = 1.62 \[ \frac{a^{10} x^{5}}{5} + \frac{5 a^{9} b x^{6}}{3} + \frac{45 a^{8} b^{2} x^{7}}{7} + 15 a^{7} b^{3} x^{8} + \frac{70 a^{6} b^{4} x^{9}}{3} + \frac{126 a^{5} b^{5} x^{10}}{5} + \frac{210 a^{4} b^{6} x^{11}}{11} + 10 a^{3} b^{7} x^{12} + \frac{45 a^{2} b^{8} x^{13}}{13} + \frac{5 a b^{9} x^{14}}{7} + \frac{b^{10} x^{15}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x+a)**10,x)
[Out]
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GIAC/XCAS [A] time = 0.202547, size = 151, normalized size = 1.86 \[ \frac{1}{15} \, b^{10} x^{15} + \frac{5}{7} \, a b^{9} x^{14} + \frac{45}{13} \, a^{2} b^{8} x^{13} + 10 \, a^{3} b^{7} x^{12} + \frac{210}{11} \, a^{4} b^{6} x^{11} + \frac{126}{5} \, a^{5} b^{5} x^{10} + \frac{70}{3} \, a^{6} b^{4} x^{9} + 15 \, a^{7} b^{3} x^{8} + \frac{45}{7} \, a^{8} b^{2} x^{7} + \frac{5}{3} \, a^{9} b x^{6} + \frac{1}{5} \, a^{10} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10*x^4,x, algorithm="giac")
[Out]