Optimal. Leaf size=17 \[ \frac{x^6}{6 a (a+b x)^6} \]
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Rubi [A] time = 0.0018992, antiderivative size = 17, normalized size of antiderivative = 1., 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} \[ \frac{x^6}{6 a (a+b x)^6} \]
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*}
Mathematica [B] time = 0.0184956, size = 64, normalized size = 3.76 \[ -\frac{15 a^3 b^2 x^2+20 a^2 b^3 x^3+6 a^4 b x+a^5+15 a b^4 x^4+6 b^5 x^5}{6 b^6 (a+b x)^6} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.007, size = 87, normalized size = 5.1 \begin{align*} -{\frac{{a}^{4}}{{b}^{6} \left ( bx+a \right ) ^{5}}}-{\frac{1}{{b}^{6} \left ( bx+a \right ) }}+{\frac{5\,{a}^{3}}{2\,{b}^{6} \left ( bx+a \right ) ^{4}}}+{\frac{5\,a}{2\,{b}^{6} \left ( bx+a \right ) ^{2}}}+{\frac{{a}^{5}}{6\,{b}^{6} \left ( bx+a \right ) ^{6}}}-{\frac{10\,{a}^{2}}{3\,{b}^{6} \left ( bx+a \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.06284, size = 162, normalized size = 9.53 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.4968, size = 252, normalized size = 14.82 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.99007, size = 128, normalized size = 7.53 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.18808, size = 84, normalized size = 4.94 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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