Optimal. Leaf size=17 \[ -\frac {(a+b x)^4}{4 a x^4} \]
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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)^4}{4 a x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^5} \, dx &=-\frac {(a+b x)^4}{4 a x^4}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(39\) vs. \(2(17)=34\).
time = 0.00, size = 39, normalized size = 2.29 \begin {gather*} -\frac {a^3}{4 x^4}-\frac {a^2 b}{x^3}-\frac {3 a b^2}{2 x^2}-\frac {b^3}{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. \(35\) vs.
\(2(15)=30\).
time = 0.07, size = 36, normalized size = 2.12
method | result | size |
gosper | \(-\frac {4 b^{3} x^{3}+6 a \,b^{2} x^{2}+4 a^{2} b x +a^{3}}{4 x^{4}}\) | \(34\) |
norman | \(\frac {-b^{3} x^{3}-\frac {3}{2} a \,b^{2} x^{2}-a^{2} b x -\frac {1}{4} a^{3}}{x^{4}}\) | \(35\) |
risch | \(\frac {-b^{3} x^{3}-\frac {3}{2} a \,b^{2} x^{2}-a^{2} b x -\frac {1}{4} a^{3}}{x^{4}}\) | \(35\) |
default | \(-\frac {b^{3}}{x}-\frac {a^{2} b}{x^{3}}-\frac {a^{3}}{4 x^{4}}-\frac {3 a \,b^{2}}{2 x^{2}}\) | \(36\) |
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. 33 vs.
\(2 (15) = 30\).
time = 0.27, size = 33, normalized size = 1.94 \begin {gather*} -\frac {4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \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. 33 vs.
\(2 (15) = 30\).
time = 1.02, size = 33, normalized size = 1.94 \begin {gather*} -\frac {4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \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. 36 vs.
\(2 (14) = 28\).
time = 0.08, size = 36, normalized size = 2.12 \begin {gather*} \frac {- a^{3} - 4 a^{2} b x - 6 a b^{2} x^{2} - 4 b^{3} x^{3}}{4 x^{4}} \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. 33 vs.
\(2 (15) = 30\).
time = 1.61, size = 33, normalized size = 1.94 \begin {gather*} -\frac {4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 33, normalized size = 1.94 \begin {gather*} -\frac {\frac {a^3}{4}+a^2\,b\,x+\frac {3\,a\,b^2\,x^2}{2}+b^3\,x^3}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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