Optimal. Leaf size=21 \[ -\frac{\left (a+b \sqrt{x}\right )^{16}}{8 a x^8} \]
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Rubi [A] time = 0.0032669, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{\left (a+b \sqrt{x}\right )^{16}}{8 a x^8} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt{x}\right )^{15}}{x^9} \, dx &=-\frac{\left (a+b \sqrt{x}\right )^{16}}{8 a x^8}\\ \end{align*}
Mathematica [A] time = 0.0070721, size = 21, normalized size = 1. \[ -\frac{\left (a+b \sqrt{x}\right )^{16}}{8 a x^8} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.004, size = 168, normalized size = 8. \begin{align*} -2\,{\frac{{b}^{15}}{\sqrt{x}}}-15\,{\frac{a{b}^{14}}{x}}-70\,{\frac{{a}^{2}{b}^{13}}{{x}^{3/2}}}-{\frac{455\,{a}^{3}{b}^{12}}{2\,{x}^{2}}}-546\,{\frac{{a}^{4}{b}^{11}}{{x}^{5/2}}}-1001\,{\frac{{a}^{5}{b}^{10}}{{x}^{3}}}-1430\,{\frac{{a}^{6}{b}^{9}}{{x}^{7/2}}}-{\frac{6435\,{a}^{7}{b}^{8}}{4\,{x}^{4}}}-1430\,{\frac{{a}^{8}{b}^{7}}{{x}^{9/2}}}-1001\,{\frac{{a}^{9}{b}^{6}}{{x}^{5}}}-546\,{\frac{{a}^{10}{b}^{5}}{{x}^{11/2}}}-{\frac{455\,{a}^{11}{b}^{4}}{2\,{x}^{6}}}-70\,{\frac{{a}^{12}{b}^{3}}{{x}^{13/2}}}-15\,{\frac{{a}^{13}{b}^{2}}{{x}^{7}}}-2\,{\frac{{a}^{14}b}{{x}^{15/2}}}-{\frac{{a}^{15}}{8\,{x}^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.969159, size = 223, normalized size = 10.62 \begin{align*} -\frac{16 \, b^{15} x^{\frac{15}{2}} + 120 \, a b^{14} x^{7} + 560 \, a^{2} b^{13} x^{\frac{13}{2}} + 1820 \, a^{3} b^{12} x^{6} + 4368 \, a^{4} b^{11} x^{\frac{11}{2}} + 8008 \, a^{5} b^{10} x^{5} + 11440 \, a^{6} b^{9} x^{\frac{9}{2}} + 12870 \, a^{7} b^{8} x^{4} + 11440 \, a^{8} b^{7} x^{\frac{7}{2}} + 8008 \, a^{9} b^{6} x^{3} + 4368 \, a^{10} b^{5} x^{\frac{5}{2}} + 1820 \, a^{11} b^{4} x^{2} + 560 \, a^{12} b^{3} x^{\frac{3}{2}} + 120 \, a^{13} b^{2} x + 16 \, a^{14} b \sqrt{x} + a^{15}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.24662, size = 393, normalized size = 18.71 \begin{align*} -\frac{120 \, a b^{14} x^{7} + 1820 \, a^{3} b^{12} x^{6} + 8008 \, a^{5} b^{10} x^{5} + 12870 \, a^{7} b^{8} x^{4} + 8008 \, a^{9} b^{6} x^{3} + 1820 \, a^{11} b^{4} x^{2} + 120 \, a^{13} b^{2} x + a^{15} + 16 \,{\left (b^{15} x^{7} + 35 \, a^{2} b^{13} x^{6} + 273 \, a^{4} b^{11} x^{5} + 715 \, a^{6} b^{9} x^{4} + 715 \, a^{8} b^{7} x^{3} + 273 \, a^{10} b^{5} x^{2} + 35 \, a^{12} b^{3} x + a^{14} b\right )} \sqrt{x}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 6.76106, size = 197, normalized size = 9.38 \begin{align*} - \frac{a^{15}}{8 x^{8}} - \frac{2 a^{14} b}{x^{\frac{15}{2}}} - \frac{15 a^{13} b^{2}}{x^{7}} - \frac{70 a^{12} b^{3}}{x^{\frac{13}{2}}} - \frac{455 a^{11} b^{4}}{2 x^{6}} - \frac{546 a^{10} b^{5}}{x^{\frac{11}{2}}} - \frac{1001 a^{9} b^{6}}{x^{5}} - \frac{1430 a^{8} b^{7}}{x^{\frac{9}{2}}} - \frac{6435 a^{7} b^{8}}{4 x^{4}} - \frac{1430 a^{6} b^{9}}{x^{\frac{7}{2}}} - \frac{1001 a^{5} b^{10}}{x^{3}} - \frac{546 a^{4} b^{11}}{x^{\frac{5}{2}}} - \frac{455 a^{3} b^{12}}{2 x^{2}} - \frac{70 a^{2} b^{13}}{x^{\frac{3}{2}}} - \frac{15 a b^{14}}{x} - \frac{2 b^{15}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.10753, size = 223, normalized size = 10.62 \begin{align*} -\frac{16 \, b^{15} x^{\frac{15}{2}} + 120 \, a b^{14} x^{7} + 560 \, a^{2} b^{13} x^{\frac{13}{2}} + 1820 \, a^{3} b^{12} x^{6} + 4368 \, a^{4} b^{11} x^{\frac{11}{2}} + 8008 \, a^{5} b^{10} x^{5} + 11440 \, a^{6} b^{9} x^{\frac{9}{2}} + 12870 \, a^{7} b^{8} x^{4} + 11440 \, a^{8} b^{7} x^{\frac{7}{2}} + 8008 \, a^{9} b^{6} x^{3} + 4368 \, a^{10} b^{5} x^{\frac{5}{2}} + 1820 \, a^{11} b^{4} x^{2} + 560 \, a^{12} b^{3} x^{\frac{3}{2}} + 120 \, a^{13} b^{2} x + 16 \, a^{14} b \sqrt{x} + a^{15}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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