Optimal. Leaf size=62 \[ -\frac{b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}}+\frac{b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac{\left (a+b x^3\right )^6}{24 a x^{24}} \]
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Rubi [A] time = 0.0280182, antiderivative size = 62, normalized size of antiderivative = 1., 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 = {266, 45, 37} \[ -\frac{b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}}+\frac{b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac{\left (a+b x^3\right )^6}{24 a x^{24}} \]
Antiderivative was successfully verified.
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Rule 266
Rule 45
Rule 37
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5}{x^{25}} \, dx &=\frac{1}{3} \operatorname{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 \operatorname{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 \operatorname{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*}
Mathematica [A] time = 0.0067473, size = 69, normalized size = 1.11 \[ -\frac{5 a^3 b^2}{9 x^{18}}-\frac{2 a^2 b^3}{3 x^{15}}-\frac{5 a^4 b}{21 x^{21}}-\frac{a^5}{24 x^{24}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{9 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 58, normalized size = 0.9 \begin{align*} -{\frac{5\,a{b}^{4}}{12\,{x}^{12}}}-{\frac{5\,{a}^{4}b}{21\,{x}^{21}}}-{\frac{2\,{a}^{2}{b}^{3}}{3\,{x}^{15}}}-{\frac{{a}^{5}}{24\,{x}^{24}}}-{\frac{5\,{a}^{3}{b}^{2}}{9\,{x}^{18}}}-{\frac{{b}^{5}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96611, size = 80, normalized size = 1.29 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49754, size = 142, normalized size = 2.29 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.982947, size = 63, normalized size = 1.02 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11518, size = 80, normalized size = 1.29 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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