Optimal. Leaf size=21 \[ -\frac {\left (a+b \sqrt {x}\right )^{16}}{8 a x^8} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ -\frac {\left (a+b \sqrt {x}\right )^{16}}{8 a x^8} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.92, size = 164, normalized size = 7.81 \[ -\frac {120 \, a b^{14} x^{7} + 1820 \, a^{3} b^{12} x^{6} + 8008 \, a^{5} b^{10} x^{5} + 12870 \, a^{7} b^{8} x^{4} + 8008 \, a^{9} b^{6} x^{3} + 1820 \, a^{11} b^{4} x^{2} + 120 \, a^{13} b^{2} x + a^{15} + 16 \, {\left (b^{15} x^{7} + 35 \, a^{2} b^{13} x^{6} + 273 \, a^{4} b^{11} x^{5} + 715 \, a^{6} b^{9} x^{4} + 715 \, a^{8} b^{7} x^{3} + 273 \, a^{10} b^{5} x^{2} + 35 \, a^{12} b^{3} x + a^{14} b\right )} \sqrt {x}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.19, size = 165, normalized size = 7.86 \[ -\frac {16 \, b^{15} x^{\frac {15}{2}} + 120 \, a b^{14} x^{7} + 560 \, a^{2} b^{13} x^{\frac {13}{2}} + 1820 \, a^{3} b^{12} x^{6} + 4368 \, a^{4} b^{11} x^{\frac {11}{2}} + 8008 \, a^{5} b^{10} x^{5} + 11440 \, a^{6} b^{9} x^{\frac {9}{2}} + 12870 \, a^{7} b^{8} x^{4} + 11440 \, a^{8} b^{7} x^{\frac {7}{2}} + 8008 \, a^{9} b^{6} x^{3} + 4368 \, a^{10} b^{5} x^{\frac {5}{2}} + 1820 \, a^{11} b^{4} x^{2} + 560 \, a^{12} b^{3} x^{\frac {3}{2}} + 120 \, a^{13} b^{2} x + 16 \, a^{14} b \sqrt {x} + a^{15}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 168, normalized size = 8.00 \[ -\frac {2 b^{15}}{\sqrt {x}}-\frac {15 a \,b^{14}}{x}-\frac {70 a^{2} b^{13}}{x^{\frac {3}{2}}}-\frac {455 a^{3} b^{12}}{2 x^{2}}-\frac {546 a^{4} b^{11}}{x^{\frac {5}{2}}}-\frac {1001 a^{5} b^{10}}{x^{3}}-\frac {1430 a^{6} b^{9}}{x^{\frac {7}{2}}}-\frac {6435 a^{7} b^{8}}{4 x^{4}}-\frac {1430 a^{8} b^{7}}{x^{\frac {9}{2}}}-\frac {1001 a^{9} b^{6}}{x^{5}}-\frac {546 a^{10} b^{5}}{x^{\frac {11}{2}}}-\frac {455 a^{11} b^{4}}{2 x^{6}}-\frac {70 a^{12} b^{3}}{x^{\frac {13}{2}}}-\frac {15 a^{13} b^{2}}{x^{7}}-\frac {2 a^{14} b}{x^{\frac {15}{2}}}-\frac {a^{15}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.96, size = 165, normalized size = 7.86 \[ -\frac {16 \, b^{15} x^{\frac {15}{2}} + 120 \, a b^{14} x^{7} + 560 \, a^{2} b^{13} x^{\frac {13}{2}} + 1820 \, a^{3} b^{12} x^{6} + 4368 \, a^{4} b^{11} x^{\frac {11}{2}} + 8008 \, a^{5} b^{10} x^{5} + 11440 \, a^{6} b^{9} x^{\frac {9}{2}} + 12870 \, a^{7} b^{8} x^{4} + 11440 \, a^{8} b^{7} x^{\frac {7}{2}} + 8008 \, a^{9} b^{6} x^{3} + 4368 \, a^{10} b^{5} x^{\frac {5}{2}} + 1820 \, a^{11} b^{4} x^{2} + 560 \, a^{12} b^{3} x^{\frac {3}{2}} + 120 \, a^{13} b^{2} x + 16 \, a^{14} b \sqrt {x} + a^{15}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 167, normalized size = 7.95 \[ -\frac {\frac {a^{15}}{8}+2\,b^{15}\,x^{15/2}+15\,a^{13}\,b^2\,x+2\,a^{14}\,b\,\sqrt {x}+15\,a\,b^{14}\,x^7+\frac {455\,a^{11}\,b^4\,x^2}{2}+1001\,a^9\,b^6\,x^3+\frac {6435\,a^7\,b^8\,x^4}{4}+1001\,a^5\,b^{10}\,x^5+70\,a^{12}\,b^3\,x^{3/2}+\frac {455\,a^3\,b^{12}\,x^6}{2}+546\,a^{10}\,b^5\,x^{5/2}+1430\,a^8\,b^7\,x^{7/2}+1430\,a^6\,b^9\,x^{9/2}+546\,a^4\,b^{11}\,x^{11/2}+70\,a^2\,b^{13}\,x^{13/2}}{x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 7.56, size = 197, normalized size = 9.38 \[ - \frac {a^{15}}{8 x^{8}} - \frac {2 a^{14} b}{x^{\frac {15}{2}}} - \frac {15 a^{13} b^{2}}{x^{7}} - \frac {70 a^{12} b^{3}}{x^{\frac {13}{2}}} - \frac {455 a^{11} b^{4}}{2 x^{6}} - \frac {546 a^{10} b^{5}}{x^{\frac {11}{2}}} - \frac {1001 a^{9} b^{6}}{x^{5}} - \frac {1430 a^{8} b^{7}}{x^{\frac {9}{2}}} - \frac {6435 a^{7} b^{8}}{4 x^{4}} - \frac {1430 a^{6} b^{9}}{x^{\frac {7}{2}}} - \frac {1001 a^{5} b^{10}}{x^{3}} - \frac {546 a^{4} b^{11}}{x^{\frac {5}{2}}} - \frac {455 a^{3} b^{12}}{2 x^{2}} - \frac {70 a^{2} b^{13}}{x^{\frac {3}{2}}} - \frac {15 a b^{14}}{x} - \frac {2 b^{15}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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