Optimal. Leaf size=61 \[ a^5 x+\frac {5}{4} a^4 b x^4+\frac {10}{7} a^3 b^2 x^7+a^2 b^3 x^{10}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{16}}{16} \]
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Rubi [A] time = 0.02, antiderivative size = 61, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {194} \[ a^2 b^3 x^{10}+\frac {10}{7} a^3 b^2 x^7+\frac {5}{4} a^4 b x^4+a^5 x+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{16}}{16} \]
Antiderivative was successfully verified.
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Rule 194
Rubi steps
\begin {align*} \int \left (a+b x^3\right )^5 \, dx &=\int \left (a^5+5 a^4 b x^3+10 a^3 b^2 x^6+10 a^2 b^3 x^9+5 a b^4 x^{12}+b^5 x^{15}\right ) \, dx\\ &=a^5 x+\frac {5}{4} a^4 b x^4+\frac {10}{7} a^3 b^2 x^7+a^2 b^3 x^{10}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{16}}{16}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 61, normalized size = 1.00 \[ a^5 x+\frac {5}{4} a^4 b x^4+\frac {10}{7} a^3 b^2 x^7+a^2 b^3 x^{10}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{16}}{16} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 53, normalized size = 0.87 \[ \frac {1}{16} x^{16} b^{5} + \frac {5}{13} x^{13} b^{4} a + x^{10} b^{3} a^{2} + \frac {10}{7} x^{7} b^{2} a^{3} + \frac {5}{4} x^{4} b a^{4} + x a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 53, normalized size = 0.87 \[ \frac {1}{16} \, b^{5} x^{16} + \frac {5}{13} \, a b^{4} x^{13} + a^{2} b^{3} x^{10} + \frac {10}{7} \, a^{3} b^{2} x^{7} + \frac {5}{4} \, a^{4} b x^{4} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 54, normalized size = 0.89 \[ \frac {1}{16} b^{5} x^{16}+\frac {5}{13} a \,b^{4} x^{13}+a^{2} b^{3} x^{10}+\frac {10}{7} a^{3} b^{2} x^{7}+\frac {5}{4} a^{4} b \,x^{4}+a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 53, normalized size = 0.87 \[ \frac {1}{16} \, b^{5} x^{16} + \frac {5}{13} \, a b^{4} x^{13} + a^{2} b^{3} x^{10} + \frac {10}{7} \, a^{3} b^{2} x^{7} + \frac {5}{4} \, a^{4} b x^{4} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 53, normalized size = 0.87 \[ a^5\,x+\frac {5\,a^4\,b\,x^4}{4}+\frac {10\,a^3\,b^2\,x^7}{7}+a^2\,b^3\,x^{10}+\frac {5\,a\,b^4\,x^{13}}{13}+\frac {b^5\,x^{16}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 60, normalized size = 0.98 \[ a^{5} x + \frac {5 a^{4} b x^{4}}{4} + \frac {10 a^{3} b^{2} x^{7}}{7} + a^{2} b^{3} x^{10} + \frac {5 a b^{4} x^{13}}{13} + \frac {b^{5} x^{16}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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