Optimal. Leaf size=62 \[ -\frac {\left (a+b x^3\right )^6}{24 a x^{24}}+\frac {b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac {b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}} \]
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Rubi [A]
time = 0.02, antiderivative size = 62, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {272, 47, 37}
\begin {gather*} -\frac {b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}}+\frac {b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac {\left (a+b x^3\right )^6}{24 a x^{24}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 47
Rule 272
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^{25}} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^5}{x^9} \, dx,x,x^3\right )\\ &=-\frac {\left (a+b x^3\right )^6}{24 a x^{24}}-\frac {b \text {Subst}\left (\int \frac {(a+b x)^5}{x^8} \, dx,x,x^3\right )}{12 a}\\ &=-\frac {\left (a+b x^3\right )^6}{24 a x^{24}}+\frac {b \left (a+b x^3\right )^6}{84 a^2 x^{21}}+\frac {b^2 \text {Subst}\left (\int \frac {(a+b x)^5}{x^7} \, dx,x,x^3\right )}{84 a^2}\\ &=-\frac {\left (a+b x^3\right )^6}{24 a x^{24}}+\frac {b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac {b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 69, normalized size = 1.11 \begin {gather*} -\frac {a^5}{24 x^{24}}-\frac {5 a^4 b}{21 x^{21}}-\frac {5 a^3 b^2}{9 x^{18}}-\frac {2 a^2 b^3}{3 x^{15}}-\frac {5 a b^4}{12 x^{12}}-\frac {b^5}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 58, normalized size = 0.94
method | result | size |
default | \(-\frac {2 a^{2} b^{3}}{3 x^{15}}-\frac {b^{5}}{9 x^{9}}-\frac {5 a \,b^{4}}{12 x^{12}}-\frac {5 a^{4} b}{21 x^{21}}-\frac {a^{5}}{24 x^{24}}-\frac {5 a^{3} b^{2}}{9 x^{18}}\) | \(58\) |
norman | \(\frac {-\frac {1}{9} b^{5} x^{15}-\frac {2}{3} a^{2} b^{3} x^{9}-\frac {5}{12} a \,b^{4} x^{12}-\frac {5}{21} a^{4} b \,x^{3}-\frac {5}{9} a^{3} b^{2} x^{6}-\frac {1}{24} a^{5}}{x^{24}}\) | \(59\) |
risch | \(\frac {-\frac {1}{9} b^{5} x^{15}-\frac {2}{3} a^{2} b^{3} x^{9}-\frac {5}{12} a \,b^{4} x^{12}-\frac {5}{21} a^{4} b \,x^{3}-\frac {5}{9} a^{3} b^{2} x^{6}-\frac {1}{24} a^{5}}{x^{24}}\) | \(59\) |
gosper | \(-\frac {56 b^{5} x^{15}+210 a \,b^{4} x^{12}+336 a^{2} b^{3} x^{9}+280 a^{3} b^{2} x^{6}+120 a^{4} b \,x^{3}+21 a^{5}}{504 x^{24}}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 59, normalized size = 0.95 \begin {gather*} -\frac {56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 59, normalized size = 0.95 \begin {gather*} -\frac {56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.29, size = 63, normalized size = 1.02 \begin {gather*} \frac {- 21 a^{5} - 120 a^{4} b x^{3} - 280 a^{3} b^{2} x^{6} - 336 a^{2} b^{3} x^{9} - 210 a b^{4} x^{12} - 56 b^{5} x^{15}}{504 x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.16, size = 59, normalized size = 0.95 \begin {gather*} -\frac {56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.95, size = 59, normalized size = 0.95 \begin {gather*} -\frac {\frac {a^5}{24}+\frac {5\,a^4\,b\,x^3}{21}+\frac {5\,a^3\,b^2\,x^6}{9}+\frac {2\,a^2\,b^3\,x^9}{3}+\frac {5\,a\,b^4\,x^{12}}{12}+\frac {b^5\,x^{15}}{9}}{x^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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