Optimal. Leaf size=77 \[ \frac {80 x^{7/2}}{567}+\frac {400 x^{5/2}}{6561}+\frac {50000 x^{3/2}}{1594323}+\frac {2 x^4}{9}+\frac {200 x^3}{2187}+\frac {2500 x^2}{59049}+\frac {125000 x}{4782969}-\frac {56145628 \sqrt {x}}{43046721}-\frac {280728140 \log \left (5-9 \sqrt {x}\right )}{387420489} \]
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Rubi [A] time = 0.07, antiderivative size = 77, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 4, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.190, Rules used = {1893, 190, 43, 266} \[ \frac {2 x^4}{9}+\frac {80 x^{7/2}}{567}+\frac {200 x^3}{2187}+\frac {400 x^{5/2}}{6561}+\frac {2500 x^2}{59049}+\frac {50000 x^{3/2}}{1594323}+\frac {125000 x}{4782969}-\frac {56145628 \sqrt {x}}{43046721}-\frac {280728140 \log \left (5-9 \sqrt {x}\right )}{387420489} \]
Antiderivative was successfully verified.
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Rule 43
Rule 190
Rule 266
Rule 1893
Rubi steps
\begin {align*} \int \frac {6-8 x^{7/2}}{5-9 \sqrt {x}} \, dx &=\int \left (-\frac {6}{-5+9 \sqrt {x}}+\frac {8 x^{7/2}}{-5+9 \sqrt {x}}\right ) \, dx\\ &=-\left (6 \int \frac {1}{-5+9 \sqrt {x}} \, dx\right )+8 \int \frac {x^{7/2}}{-5+9 \sqrt {x}} \, dx\\ &=-\left (12 \operatorname {Subst}\left (\int \frac {x}{-5+9 x} \, dx,x,\sqrt {x}\right )\right )+16 \operatorname {Subst}\left (\int \frac {x^8}{-5+9 x} \, dx,x,\sqrt {x}\right )\\ &=-\left (12 \operatorname {Subst}\left (\int \left (\frac {1}{9}+\frac {5}{9 (-5+9 x)}\right ) \, dx,x,\sqrt {x}\right )\right )+16 \operatorname {Subst}\left (\int \left (\frac {78125}{43046721}+\frac {15625 x}{4782969}+\frac {3125 x^2}{531441}+\frac {625 x^3}{59049}+\frac {125 x^4}{6561}+\frac {25 x^5}{729}+\frac {5 x^6}{81}+\frac {x^7}{9}+\frac {390625}{43046721 (-5+9 x)}\right ) \, dx,x,\sqrt {x}\right )\\ &=-\frac {56145628 \sqrt {x}}{43046721}+\frac {125000 x}{4782969}+\frac {50000 x^{3/2}}{1594323}+\frac {2500 x^2}{59049}+\frac {400 x^{5/2}}{6561}+\frac {200 x^3}{2187}+\frac {80 x^{7/2}}{567}+\frac {2 x^4}{9}-\frac {280728140 \log \left (5-9 \sqrt {x}\right )}{387420489}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 66, normalized size = 0.86 \[ \frac {2 \left (9 \left (21257640 x^{7/2}+9185400 x^{5/2}+4725000 x^{3/2}+33480783 x^4+13778100 x^3+6378750 x^2+3937500 x-196509698 \sqrt {x}\right )-982548490 \log \left (5-9 \sqrt {x}\right )\right )}{2711943423} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 49, normalized size = 0.64 \[ \frac {2}{9} \, x^{4} + \frac {200}{2187} \, x^{3} + \frac {2500}{59049} \, x^{2} + \frac {4}{301327047} \, {\left (10628820 \, x^{3} + 4592700 \, x^{2} + 2362500 \, x - 98254849\right )} \sqrt {x} + \frac {125000}{4782969} \, x - \frac {280728140}{387420489} \, \log \left (9 \, \sqrt {x} - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 50, normalized size = 0.65 \[ \frac {2}{9} \, x^{4} + \frac {80}{567} \, x^{\frac {7}{2}} + \frac {200}{2187} \, x^{3} + \frac {400}{6561} \, x^{\frac {5}{2}} + \frac {2500}{59049} \, x^{2} + \frac {50000}{1594323} \, x^{\frac {3}{2}} + \frac {125000}{4782969} \, x - \frac {56145628}{43046721} \, \sqrt {x} - \frac {280728140}{387420489} \, \log \left ({\left | 9 \, \sqrt {x} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 50, normalized size = 0.65 \[ \frac {2 x^{4}}{9}+\frac {80 x^{\frac {7}{2}}}{567}+\frac {200 x^{3}}{2187}+\frac {400 x^{\frac {5}{2}}}{6561}+\frac {2500 x^{2}}{59049}+\frac {50000 x^{\frac {3}{2}}}{1594323}+\frac {125000 x}{4782969}-\frac {280728140 \ln \left (9 \sqrt {x}-5\right )}{387420489}-\frac {56145628 \sqrt {x}}{43046721} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 49, normalized size = 0.64 \[ \frac {2}{9} \, x^{4} + \frac {80}{567} \, x^{\frac {7}{2}} + \frac {200}{2187} \, x^{3} + \frac {400}{6561} \, x^{\frac {5}{2}} + \frac {2500}{59049} \, x^{2} + \frac {50000}{1594323} \, x^{\frac {3}{2}} + \frac {125000}{4782969} \, x - \frac {56145628}{43046721} \, \sqrt {x} - \frac {280728140}{387420489} \, \log \left (9 \, \sqrt {x} - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 47, normalized size = 0.61 \[ \frac {125000\,x}{4782969}-\frac {280728140\,\ln \left (\sqrt {x}-\frac {5}{9}\right )}{387420489}+\frac {2500\,x^2}{59049}-\frac {56145628\,\sqrt {x}}{43046721}+\frac {200\,x^3}{2187}+\frac {2\,x^4}{9}+\frac {50000\,x^{3/2}}{1594323}+\frac {400\,x^{5/2}}{6561}+\frac {80\,x^{7/2}}{567} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.32, size = 71, normalized size = 0.92 \[ \frac {80 x^{\frac {7}{2}}}{567} + \frac {400 x^{\frac {5}{2}}}{6561} + \frac {50000 x^{\frac {3}{2}}}{1594323} - \frac {56145628 \sqrt {x}}{43046721} + \frac {2 x^{4}}{9} + \frac {200 x^{3}}{2187} + \frac {2500 x^{2}}{59049} + \frac {125000 x}{4782969} - \frac {280728140 \log {\left (\sqrt {x} - \frac {5}{9} \right )}}{387420489} \]
Verification of antiderivative is not currently implemented for this CAS.
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