Optimal. Leaf size=65 \[ -\frac {a^5}{x}+\frac {5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac {5}{4} a^2 b^3 x^8+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{14}}{14} \]
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Rubi [A]
time = 0.02, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276}
\begin {gather*} -\frac {a^5}{x}+\frac {5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac {5}{4} a^2 b^3 x^8+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{14}}{14} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^2} \, dx &=\int \left (\frac {a^5}{x^2}+5 a^4 b x+10 a^3 b^2 x^4+10 a^2 b^3 x^7+5 a b^4 x^{10}+b^5 x^{13}\right ) \, dx\\ &=-\frac {a^5}{x}+\frac {5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac {5}{4} a^2 b^3 x^8+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{14}}{14}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 65, normalized size = 1.00 \begin {gather*} -\frac {a^5}{x}+\frac {5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac {5}{4} a^2 b^3 x^8+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{14}}{14} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 58, normalized size = 0.89
method | result | size |
default | \(-\frac {a^{5}}{x}+\frac {5 a^{4} b \,x^{2}}{2}+2 a^{3} b^{2} x^{5}+\frac {5 a^{2} b^{3} x^{8}}{4}+\frac {5 a \,b^{4} x^{11}}{11}+\frac {b^{5} x^{14}}{14}\) | \(58\) |
risch | \(-\frac {a^{5}}{x}+\frac {5 a^{4} b \,x^{2}}{2}+2 a^{3} b^{2} x^{5}+\frac {5 a^{2} b^{3} x^{8}}{4}+\frac {5 a \,b^{4} x^{11}}{11}+\frac {b^{5} x^{14}}{14}\) | \(58\) |
norman | \(\frac {-a^{5}+\frac {5}{2} a^{4} b \,x^{3}+2 a^{3} b^{2} x^{6}+\frac {5}{4} a^{2} b^{3} x^{9}+\frac {5}{11} a \,b^{4} x^{12}+\frac {1}{14} b^{5} x^{15}}{x}\) | \(59\) |
gosper | \(-\frac {-22 b^{5} x^{15}-140 a \,b^{4} x^{12}-385 a^{2} b^{3} x^{9}-616 a^{3} b^{2} x^{6}-770 a^{4} b \,x^{3}+308 a^{5}}{308 x}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 57, normalized size = 0.88 \begin {gather*} \frac {1}{14} \, b^{5} x^{14} + \frac {5}{11} \, a b^{4} x^{11} + \frac {5}{4} \, a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{5} + \frac {5}{2} \, a^{4} b x^{2} - \frac {a^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 59, normalized size = 0.91 \begin {gather*} \frac {22 \, b^{5} x^{15} + 140 \, a b^{4} x^{12} + 385 \, a^{2} b^{3} x^{9} + 616 \, a^{3} b^{2} x^{6} + 770 \, a^{4} b x^{3} - 308 \, a^{5}}{308 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 61, normalized size = 0.94 \begin {gather*} - \frac {a^{5}}{x} + \frac {5 a^{4} b x^{2}}{2} + 2 a^{3} b^{2} x^{5} + \frac {5 a^{2} b^{3} x^{8}}{4} + \frac {5 a b^{4} x^{11}}{11} + \frac {b^{5} x^{14}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.23, size = 57, normalized size = 0.88 \begin {gather*} \frac {1}{14} \, b^{5} x^{14} + \frac {5}{11} \, a b^{4} x^{11} + \frac {5}{4} \, a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{5} + \frac {5}{2} \, a^{4} b x^{2} - \frac {a^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 57, normalized size = 0.88 \begin {gather*} \frac {b^5\,x^{14}}{14}-\frac {a^5}{x}+\frac {5\,a^4\,b\,x^2}{2}+\frac {5\,a\,b^4\,x^{11}}{11}+2\,a^3\,b^2\,x^5+\frac {5\,a^2\,b^3\,x^8}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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