Optimal. Leaf size=36 \[ \frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9} \]
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Rubi [A] time = 0.0048768, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {45, 37} \[ \frac{b (a+b x)^8}{72 a^2 x^8}-\frac{(a+b x)^8}{9 a x^9} \]
Antiderivative was successfully verified.
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Rule 45
Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^7}{x^{10}} \, dx &=-\frac{(a+b x)^8}{9 a x^9}-\frac{b \int \frac{(a+b x)^7}{x^9} \, dx}{9 a}\\ &=-\frac{(a+b x)^8}{9 a x^9}+\frac{b (a+b x)^8}{72 a^2 x^8}\\ \end{align*}
Mathematica [B] time = 0.0039336, size = 91, normalized size = 2.53 \[ -\frac{3 a^5 b^2}{x^7}-\frac{35 a^4 b^3}{6 x^6}-\frac{7 a^3 b^4}{x^5}-\frac{21 a^2 b^5}{4 x^4}-\frac{7 a^6 b}{8 x^8}-\frac{a^7}{9 x^9}-\frac{7 a b^6}{3 x^3}-\frac{b^7}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 80, normalized size = 2.2 \begin{align*} -{\frac{7\,a{b}^{6}}{3\,{x}^{3}}}-7\,{\frac{{a}^{3}{b}^{4}}{{x}^{5}}}-{\frac{21\,{a}^{2}{b}^{5}}{4\,{x}^{4}}}-{\frac{35\,{a}^{4}{b}^{3}}{6\,{x}^{6}}}-{\frac{7\,{a}^{6}b}{8\,{x}^{8}}}-{\frac{{b}^{7}}{2\,{x}^{2}}}-3\,{\frac{{a}^{5}{b}^{2}}{{x}^{7}}}-{\frac{{a}^{7}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.03955, size = 107, normalized size = 2.97 \begin{align*} -\frac{36 \, b^{7} x^{7} + 168 \, a b^{6} x^{6} + 378 \, a^{2} b^{5} x^{5} + 504 \, a^{3} b^{4} x^{4} + 420 \, a^{4} b^{3} x^{3} + 216 \, a^{5} b^{2} x^{2} + 63 \, a^{6} b x + 8 \, a^{7}}{72 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.72973, size = 180, normalized size = 5. \begin{align*} -\frac{36 \, b^{7} x^{7} + 168 \, a b^{6} x^{6} + 378 \, a^{2} b^{5} x^{5} + 504 \, a^{3} b^{4} x^{4} + 420 \, a^{4} b^{3} x^{3} + 216 \, a^{5} b^{2} x^{2} + 63 \, a^{6} b x + 8 \, a^{7}}{72 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.826221, size = 85, normalized size = 2.36 \begin{align*} - \frac{8 a^{7} + 63 a^{6} b x + 216 a^{5} b^{2} x^{2} + 420 a^{4} b^{3} x^{3} + 504 a^{3} b^{4} x^{4} + 378 a^{2} b^{5} x^{5} + 168 a b^{6} x^{6} + 36 b^{7} x^{7}}{72 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.19416, size = 107, normalized size = 2.97 \begin{align*} -\frac{36 \, b^{7} x^{7} + 168 \, a b^{6} x^{6} + 378 \, a^{2} b^{5} x^{5} + 504 \, a^{3} b^{4} x^{4} + 420 \, a^{4} b^{3} x^{3} + 216 \, a^{5} b^{2} x^{2} + 63 \, a^{6} b x + 8 \, a^{7}}{72 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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