Optimal. Leaf size=17 \[ -\frac {(a+b x)^6}{6 a x^6} \]
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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 {(a+b x)^6}{6 a x^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{x^7} \, dx &=-\frac {(a+b x)^6}{6 a x^6}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(17)=34\).
time = 0.00, size = 65, normalized size = 3.82 \begin {gather*} -\frac {a^5}{6 x^6}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{2 x^4}-\frac {10 a^2 b^3}{3 x^3}-\frac {5 a b^4}{2 x^2}-\frac {b^5}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs.
\(2(15)=30\).
time = 0.08, size = 58, normalized size = 3.41
method | result | size |
gosper | \(-\frac {6 b^{5} x^{5}+15 a \,b^{4} x^{4}+20 a^{2} b^{3} x^{3}+15 a^{3} b^{2} x^{2}+6 a^{4} b x +a^{5}}{6 x^{6}}\) | \(56\) |
norman | \(\frac {-b^{5} x^{5}-\frac {5}{2} a \,b^{4} x^{4}-\frac {10}{3} a^{2} b^{3} x^{3}-\frac {5}{2} a^{3} b^{2} x^{2}-a^{4} b x -\frac {1}{6} a^{5}}{x^{6}}\) | \(57\) |
risch | \(\frac {-b^{5} x^{5}-\frac {5}{2} a \,b^{4} x^{4}-\frac {10}{3} a^{2} b^{3} x^{3}-\frac {5}{2} a^{3} b^{2} x^{2}-a^{4} b x -\frac {1}{6} a^{5}}{x^{6}}\) | \(57\) |
default | \(-\frac {b^{5}}{x}-\frac {10 a^{2} b^{3}}{3 x^{3}}-\frac {5 a^{3} b^{2}}{2 x^{4}}-\frac {5 a \,b^{4}}{2 x^{2}}-\frac {a^{4} b}{x^{5}}-\frac {a^{5}}{6 x^{6}}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (15) = 30\).
time = 0.29, size = 55, normalized size = 3.24 \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 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (15) = 30\).
time = 0.54, size = 55, normalized size = 3.24 \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 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 60 vs.
\(2 (14) = 28\).
time = 0.15, size = 60, normalized size = 3.53 \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 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (15) = 30\).
time = 2.07, size = 55, normalized size = 3.24 \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 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 55, normalized size = 3.24 \begin {gather*} -\frac {\frac {a^5}{6}+a^4\,b\,x+\frac {5\,a^3\,b^2\,x^2}{2}+\frac {10\,a^2\,b^3\,x^3}{3}+\frac {5\,a\,b^4\,x^4}{2}+b^5\,x^5}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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