Optimal. Leaf size=95 \[ \frac {a^7 x^7}{7}+\frac {7}{8} a^6 b x^8+\frac {7}{3} a^5 b^2 x^9+\frac {7}{2} a^4 b^3 x^{10}+\frac {35}{11} a^3 b^4 x^{11}+\frac {7}{4} a^2 b^5 x^{12}+\frac {7}{13} a b^6 x^{13}+\frac {b^7 x^{14}}{14} \]
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Rubi [A]
time = 0.03, antiderivative size = 95, 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^7 x^7}{7}+\frac {7}{8} a^6 b x^8+\frac {7}{3} a^5 b^2 x^9+\frac {7}{2} a^4 b^3 x^{10}+\frac {35}{11} a^3 b^4 x^{11}+\frac {7}{4} a^2 b^5 x^{12}+\frac {7}{13} a b^6 x^{13}+\frac {b^7 x^{14}}{14} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^6 (a+b x)^7 \, dx &=\int \left (a^7 x^6+7 a^6 b x^7+21 a^5 b^2 x^8+35 a^4 b^3 x^9+35 a^3 b^4 x^{10}+21 a^2 b^5 x^{11}+7 a b^6 x^{12}+b^7 x^{13}\right ) \, dx\\ &=\frac {a^7 x^7}{7}+\frac {7}{8} a^6 b x^8+\frac {7}{3} a^5 b^2 x^9+\frac {7}{2} a^4 b^3 x^{10}+\frac {35}{11} a^3 b^4 x^{11}+\frac {7}{4} a^2 b^5 x^{12}+\frac {7}{13} a b^6 x^{13}+\frac {b^7 x^{14}}{14}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 95, normalized size = 1.00 \begin {gather*} \frac {a^7 x^7}{7}+\frac {7}{8} a^6 b x^8+\frac {7}{3} a^5 b^2 x^9+\frac {7}{2} a^4 b^3 x^{10}+\frac {35}{11} a^3 b^4 x^{11}+\frac {7}{4} a^2 b^5 x^{12}+\frac {7}{13} a b^6 x^{13}+\frac {b^7 x^{14}}{14} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 80, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{7} a^{7} x^{7}+\frac {7}{8} a^{6} b \,x^{8}+\frac {7}{3} a^{5} b^{2} x^{9}+\frac {7}{2} a^{4} b^{3} x^{10}+\frac {35}{11} a^{3} b^{4} x^{11}+\frac {7}{4} a^{2} b^{5} x^{12}+\frac {7}{13} a \,b^{6} x^{13}+\frac {1}{14} b^{7} x^{14}\) | \(80\) |
default | \(\frac {1}{7} a^{7} x^{7}+\frac {7}{8} a^{6} b \,x^{8}+\frac {7}{3} a^{5} b^{2} x^{9}+\frac {7}{2} a^{4} b^{3} x^{10}+\frac {35}{11} a^{3} b^{4} x^{11}+\frac {7}{4} a^{2} b^{5} x^{12}+\frac {7}{13} a \,b^{6} x^{13}+\frac {1}{14} b^{7} x^{14}\) | \(80\) |
norman | \(\frac {1}{7} a^{7} x^{7}+\frac {7}{8} a^{6} b \,x^{8}+\frac {7}{3} a^{5} b^{2} x^{9}+\frac {7}{2} a^{4} b^{3} x^{10}+\frac {35}{11} a^{3} b^{4} x^{11}+\frac {7}{4} a^{2} b^{5} x^{12}+\frac {7}{13} a \,b^{6} x^{13}+\frac {1}{14} b^{7} x^{14}\) | \(80\) |
risch | \(\frac {1}{7} a^{7} x^{7}+\frac {7}{8} a^{6} b \,x^{8}+\frac {7}{3} a^{5} b^{2} x^{9}+\frac {7}{2} a^{4} b^{3} x^{10}+\frac {35}{11} a^{3} b^{4} x^{11}+\frac {7}{4} a^{2} b^{5} x^{12}+\frac {7}{13} a \,b^{6} x^{13}+\frac {1}{14} b^{7} x^{14}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 79, normalized size = 0.83 \begin {gather*} \frac {1}{14} \, b^{7} x^{14} + \frac {7}{13} \, a b^{6} x^{13} + \frac {7}{4} \, a^{2} b^{5} x^{12} + \frac {35}{11} \, a^{3} b^{4} x^{11} + \frac {7}{2} \, a^{4} b^{3} x^{10} + \frac {7}{3} \, a^{5} b^{2} x^{9} + \frac {7}{8} \, a^{6} b x^{8} + \frac {1}{7} \, a^{7} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.99, size = 79, normalized size = 0.83 \begin {gather*} \frac {1}{14} \, b^{7} x^{14} + \frac {7}{13} \, a b^{6} x^{13} + \frac {7}{4} \, a^{2} b^{5} x^{12} + \frac {35}{11} \, a^{3} b^{4} x^{11} + \frac {7}{2} \, a^{4} b^{3} x^{10} + \frac {7}{3} \, a^{5} b^{2} x^{9} + \frac {7}{8} \, a^{6} b x^{8} + \frac {1}{7} \, a^{7} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 94, normalized size = 0.99 \begin {gather*} \frac {a^{7} x^{7}}{7} + \frac {7 a^{6} b x^{8}}{8} + \frac {7 a^{5} b^{2} x^{9}}{3} + \frac {7 a^{4} b^{3} x^{10}}{2} + \frac {35 a^{3} b^{4} x^{11}}{11} + \frac {7 a^{2} b^{5} x^{12}}{4} + \frac {7 a b^{6} x^{13}}{13} + \frac {b^{7} x^{14}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.33, size = 79, normalized size = 0.83 \begin {gather*} \frac {1}{14} \, b^{7} x^{14} + \frac {7}{13} \, a b^{6} x^{13} + \frac {7}{4} \, a^{2} b^{5} x^{12} + \frac {35}{11} \, a^{3} b^{4} x^{11} + \frac {7}{2} \, a^{4} b^{3} x^{10} + \frac {7}{3} \, a^{5} b^{2} x^{9} + \frac {7}{8} \, a^{6} b x^{8} + \frac {1}{7} \, a^{7} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 79, normalized size = 0.83 \begin {gather*} \frac {a^7\,x^7}{7}+\frac {7\,a^6\,b\,x^8}{8}+\frac {7\,a^5\,b^2\,x^9}{3}+\frac {7\,a^4\,b^3\,x^{10}}{2}+\frac {35\,a^3\,b^4\,x^{11}}{11}+\frac {7\,a^2\,b^5\,x^{12}}{4}+\frac {7\,a\,b^6\,x^{13}}{13}+\frac {b^7\,x^{14}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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