Optimal. Leaf size=66 \[ \frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12} \]
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Rubi [A]
time = 0.02, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} \frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^6 (a+b x)^5 \, dx &=\int \left (a^5 x^6+5 a^4 b x^7+10 a^3 b^2 x^8+10 a^2 b^3 x^9+5 a b^4 x^{10}+b^5 x^{11}\right ) \, dx\\ &=\frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 66, normalized size = 1.00 \begin {gather*} \frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12} \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.84, size = 57, normalized size = 0.86 \begin {gather*} \frac {x^7 \left (792 a^5+3465 a^4 b x+6160 a^3 b^2 x^2+5544 a^2 b^3 x^3+2520 a b^4 x^4+462 b^5 x^5\right )}{5544} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 57, normalized size = 0.86
method | result | size |
gosper | \(\frac {1}{7} a^{5} x^{7}+\frac {5}{8} a^{4} b \,x^{8}+\frac {10}{9} a^{3} b^{2} x^{9}+a^{2} b^{3} x^{10}+\frac {5}{11} a \,b^{4} x^{11}+\frac {1}{12} b^{5} x^{12}\) | \(57\) |
default | \(\frac {1}{7} a^{5} x^{7}+\frac {5}{8} a^{4} b \,x^{8}+\frac {10}{9} a^{3} b^{2} x^{9}+a^{2} b^{3} x^{10}+\frac {5}{11} a \,b^{4} x^{11}+\frac {1}{12} b^{5} x^{12}\) | \(57\) |
norman | \(\frac {1}{7} a^{5} x^{7}+\frac {5}{8} a^{4} b \,x^{8}+\frac {10}{9} a^{3} b^{2} x^{9}+a^{2} b^{3} x^{10}+\frac {5}{11} a \,b^{4} x^{11}+\frac {1}{12} b^{5} x^{12}\) | \(57\) |
risch | \(\frac {1}{7} a^{5} x^{7}+\frac {5}{8} a^{4} b \,x^{8}+\frac {10}{9} a^{3} b^{2} x^{9}+a^{2} b^{3} x^{10}+\frac {5}{11} a \,b^{4} x^{11}+\frac {1}{12} b^{5} x^{12}\) | \(57\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 56, normalized size = 0.85 \begin {gather*} \frac {1}{12} \, b^{5} x^{12} + \frac {5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{8} \, a^{4} b x^{8} + \frac {1}{7} \, a^{5} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 56, normalized size = 0.85 \begin {gather*} \frac {1}{12} \, b^{5} x^{12} + \frac {5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{8} \, a^{4} b x^{8} + \frac {1}{7} \, a^{5} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 63, normalized size = 0.95 \begin {gather*} \frac {a^{5} x^{7}}{7} + \frac {5 a^{4} b x^{8}}{8} + \frac {10 a^{3} b^{2} x^{9}}{9} + a^{2} b^{3} x^{10} + \frac {5 a b^{4} x^{11}}{11} + \frac {b^{5} x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 66, normalized size = 1.00 \begin {gather*} \frac {1}{12} x^{12} b^{5}+\frac {5}{11} x^{11} b^{4} a+x^{10} b^{3} a^{2}+\frac {10}{9} x^{9} b^{2} a^{3}+\frac {5}{8} x^{8} b a^{4}+\frac {1}{7} x^{7} a^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 56, normalized size = 0.85 \begin {gather*} \frac {a^5\,x^7}{7}+\frac {5\,a^4\,b\,x^8}{8}+\frac {10\,a^3\,b^2\,x^9}{9}+a^2\,b^3\,x^{10}+\frac {5\,a\,b^4\,x^{11}}{11}+\frac {b^5\,x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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