Optimal. Leaf size=35 \[ \frac {x^5}{30 a^2 (a+b x)^5}+\frac {x^5}{6 a (a+b x)^6} \]
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Rubi [A] time = 0.00, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {45, 37} \begin {gather*} \frac {x^5}{30 a^2 (a+b x)^5}+\frac {x^5}{6 a (a+b x)^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 45
Rubi steps
\begin {align*} \int \frac {x^4}{(a+b x)^7} \, dx &=\frac {x^5}{6 a (a+b x)^6}+\frac {\int \frac {x^4}{(a+b x)^6} \, dx}{6 a}\\ &=\frac {x^5}{6 a (a+b x)^6}+\frac {x^5}{30 a^2 (a+b x)^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 53, normalized size = 1.51 \begin {gather*} -\frac {a^4+6 a^3 b x+15 a^2 b^2 x^2+20 a b^3 x^3+15 b^4 x^4}{30 b^5 (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^4}{(a+b x)^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.86, size = 109, normalized size = 3.11 \begin {gather*} -\frac {15 \, b^{4} x^{4} + 20 \, a b^{3} x^{3} + 15 \, a^{2} b^{2} x^{2} + 6 \, a^{3} b x + a^{4}}{30 \, {\left (b^{11} x^{6} + 6 \, a b^{10} x^{5} + 15 \, a^{2} b^{9} x^{4} + 20 \, a^{3} b^{8} x^{3} + 15 \, a^{4} b^{7} x^{2} + 6 \, a^{5} b^{6} x + a^{6} b^{5}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 51, normalized size = 1.46 \begin {gather*} -\frac {15 \, b^{4} x^{4} + 20 \, a b^{3} x^{3} + 15 \, a^{2} b^{2} x^{2} + 6 \, a^{3} b x + a^{4}}{30 \, {\left (b x + a\right )}^{6} b^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 72, normalized size = 2.06 \begin {gather*} -\frac {a^{4}}{6 \left (b x +a \right )^{6} b^{5}}+\frac {4 a^{3}}{5 \left (b x +a \right )^{5} b^{5}}-\frac {3 a^{2}}{2 \left (b x +a \right )^{4} b^{5}}+\frac {4 a}{3 \left (b x +a \right )^{3} b^{5}}-\frac {1}{2 \left (b x +a \right )^{2} b^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.45, size = 109, normalized size = 3.11 \begin {gather*} -\frac {15 \, b^{4} x^{4} + 20 \, a b^{3} x^{3} + 15 \, a^{2} b^{2} x^{2} + 6 \, a^{3} b x + a^{4}}{30 \, {\left (b^{11} x^{6} + 6 \, a b^{10} x^{5} + 15 \, a^{2} b^{9} x^{4} + 20 \, a^{3} b^{8} x^{3} + 15 \, a^{4} b^{7} x^{2} + 6 \, a^{5} b^{6} x + a^{6} b^{5}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 22, normalized size = 0.63 \begin {gather*} \frac {x^5\,\left (6\,a+b\,x\right )}{30\,a^2\,{\left (a+b\,x\right )}^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.57, size = 116, normalized size = 3.31 \begin {gather*} \frac {- a^{4} - 6 a^{3} b x - 15 a^{2} b^{2} x^{2} - 20 a b^{3} x^{3} - 15 b^{4} x^{4}}{30 a^{6} b^{5} + 180 a^{5} b^{6} x + 450 a^{4} b^{7} x^{2} + 600 a^{3} b^{8} x^{3} + 450 a^{2} b^{9} x^{4} + 180 a b^{10} x^{5} + 30 b^{11} x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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