Optimal. Leaf size=17 \[ \frac {x^6}{6 a (a+b x)^6} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {37} \begin {gather*} \frac {x^6}{6 a (a+b x)^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {x^5}{(a+b x)^7} \, dx &=\frac {x^6}{6 a (a+b x)^6}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 64, normalized size = 3.76 \begin {gather*} -\frac {a^5+6 a^4 b x+15 a^3 b^2 x^2+20 a^2 b^3 x^3+15 a b^4 x^4+6 b^5 x^5}{6 b^6 (a+b x)^6} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^5}{(a+b x)^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.95, size = 120, normalized size = 7.06 \begin {gather*} -\frac {6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, {\left (b^{12} x^{6} + 6 \, a b^{11} x^{5} + 15 \, a^{2} b^{10} x^{4} + 20 \, a^{3} b^{9} x^{3} + 15 \, a^{4} b^{8} x^{2} + 6 \, a^{5} b^{7} x + a^{6} b^{6}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.08, size = 62, normalized size = 3.65 \begin {gather*} -\frac {6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, {\left (b x + a\right )}^{6} b^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 87, normalized size = 5.12 \begin {gather*} \frac {a^{5}}{6 \left (b x +a \right )^{6} b^{6}}-\frac {a^{4}}{\left (b x +a \right )^{5} b^{6}}+\frac {5 a^{3}}{2 \left (b x +a \right )^{4} b^{6}}-\frac {10 a^{2}}{3 \left (b x +a \right )^{3} b^{6}}+\frac {5 a}{2 \left (b x +a \right )^{2} b^{6}}-\frac {1}{\left (b x +a \right ) b^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.43, size = 120, normalized size = 7.06 \begin {gather*} -\frac {6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, {\left (b^{12} x^{6} + 6 \, a b^{11} x^{5} + 15 \, a^{2} b^{10} x^{4} + 20 \, a^{3} b^{9} x^{3} + 15 \, a^{4} b^{8} x^{2} + 6 \, a^{5} b^{7} x + a^{6} b^{6}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 72, normalized size = 4.24 \begin {gather*} \frac {\frac {5\,a}{2\,{\left (a+b\,x\right )}^2}-\frac {1}{a+b\,x}-\frac {10\,a^2}{3\,{\left (a+b\,x\right )}^3}+\frac {5\,a^3}{2\,{\left (a+b\,x\right )}^4}-\frac {a^4}{{\left (a+b\,x\right )}^5}+\frac {a^5}{6\,{\left (a+b\,x\right )}^6}}{b^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.58, size = 128, normalized size = 7.53 \begin {gather*} \frac {- a^{5} - 6 a^{4} b x - 15 a^{3} b^{2} x^{2} - 20 a^{2} b^{3} x^{3} - 15 a b^{4} x^{4} - 6 b^{5} x^{5}}{6 a^{6} b^{6} + 36 a^{5} b^{7} x + 90 a^{4} b^{8} x^{2} + 120 a^{3} b^{9} x^{3} + 90 a^{2} b^{10} x^{4} + 36 a b^{11} x^{5} + 6 b^{12} x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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