Optimal. Leaf size=136 \[ -\frac {a^{10}}{9 x^9}-\frac {20 a^9 b}{17 x^{17/2}}-\frac {45 a^8 b^2}{8 x^8}-\frac {16 a^7 b^3}{x^{15/2}}-\frac {30 a^6 b^4}{x^7}-\frac {504 a^5 b^5}{13 x^{13/2}}-\frac {35 a^4 b^6}{x^6}-\frac {240 a^3 b^7}{11 x^{11/2}}-\frac {9 a^2 b^8}{x^5}-\frac {20 a b^9}{9 x^{9/2}}-\frac {b^{10}}{4 x^4} \]
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Rubi [A] time = 0.07, antiderivative size = 136, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac {45 a^8 b^2}{8 x^8}-\frac {16 a^7 b^3}{x^{15/2}}-\frac {30 a^6 b^4}{x^7}-\frac {504 a^5 b^5}{13 x^{13/2}}-\frac {35 a^4 b^6}{x^6}-\frac {240 a^3 b^7}{11 x^{11/2}}-\frac {9 a^2 b^8}{x^5}-\frac {20 a^9 b}{17 x^{17/2}}-\frac {a^{10}}{9 x^9}-\frac {20 a b^9}{9 x^{9/2}}-\frac {b^{10}}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt {x}\right )^{10}}{x^{10}} \, dx &=2 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{19}} \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (\frac {a^{10}}{x^{19}}+\frac {10 a^9 b}{x^{18}}+\frac {45 a^8 b^2}{x^{17}}+\frac {120 a^7 b^3}{x^{16}}+\frac {210 a^6 b^4}{x^{15}}+\frac {252 a^5 b^5}{x^{14}}+\frac {210 a^4 b^6}{x^{13}}+\frac {120 a^3 b^7}{x^{12}}+\frac {45 a^2 b^8}{x^{11}}+\frac {10 a b^9}{x^{10}}+\frac {b^{10}}{x^9}\right ) \, dx,x,\sqrt {x}\right )\\ &=-\frac {a^{10}}{9 x^9}-\frac {20 a^9 b}{17 x^{17/2}}-\frac {45 a^8 b^2}{8 x^8}-\frac {16 a^7 b^3}{x^{15/2}}-\frac {30 a^6 b^4}{x^7}-\frac {504 a^5 b^5}{13 x^{13/2}}-\frac {35 a^4 b^6}{x^6}-\frac {240 a^3 b^7}{11 x^{11/2}}-\frac {9 a^2 b^8}{x^5}-\frac {20 a b^9}{9 x^{9/2}}-\frac {b^{10}}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 136, normalized size = 1.00 \[ -\frac {a^{10}}{9 x^9}-\frac {20 a^9 b}{17 x^{17/2}}-\frac {45 a^8 b^2}{8 x^8}-\frac {16 a^7 b^3}{x^{15/2}}-\frac {30 a^6 b^4}{x^7}-\frac {504 a^5 b^5}{13 x^{13/2}}-\frac {35 a^4 b^6}{x^6}-\frac {240 a^3 b^7}{11 x^{11/2}}-\frac {9 a^2 b^8}{x^5}-\frac {20 a b^9}{9 x^{9/2}}-\frac {b^{10}}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 113, normalized size = 0.83 \[ -\frac {43758 \, b^{10} x^{5} + 1575288 \, a^{2} b^{8} x^{4} + 6126120 \, a^{4} b^{6} x^{3} + 5250960 \, a^{6} b^{4} x^{2} + 984555 \, a^{8} b^{2} x + 19448 \, a^{10} + 32 \, {\left (12155 \, a b^{9} x^{4} + 119340 \, a^{3} b^{7} x^{3} + 212058 \, a^{5} b^{5} x^{2} + 87516 \, a^{7} b^{3} x + 6435 \, a^{9} b\right )} \sqrt {x}}{175032 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 112, normalized size = 0.82 \[ -\frac {43758 \, b^{10} x^{5} + 388960 \, a b^{9} x^{\frac {9}{2}} + 1575288 \, a^{2} b^{8} x^{4} + 3818880 \, a^{3} b^{7} x^{\frac {7}{2}} + 6126120 \, a^{4} b^{6} x^{3} + 6785856 \, a^{5} b^{5} x^{\frac {5}{2}} + 5250960 \, a^{6} b^{4} x^{2} + 2800512 \, a^{7} b^{3} x^{\frac {3}{2}} + 984555 \, a^{8} b^{2} x + 205920 \, a^{9} b \sqrt {x} + 19448 \, a^{10}}{175032 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 113, normalized size = 0.83 \[ -\frac {b^{10}}{4 x^{4}}-\frac {20 a \,b^{9}}{9 x^{\frac {9}{2}}}-\frac {9 a^{2} b^{8}}{x^{5}}-\frac {240 a^{3} b^{7}}{11 x^{\frac {11}{2}}}-\frac {35 a^{4} b^{6}}{x^{6}}-\frac {504 a^{5} b^{5}}{13 x^{\frac {13}{2}}}-\frac {30 a^{6} b^{4}}{x^{7}}-\frac {16 a^{7} b^{3}}{x^{\frac {15}{2}}}-\frac {45 a^{8} b^{2}}{8 x^{8}}-\frac {20 a^{9} b}{17 x^{\frac {17}{2}}}-\frac {a^{10}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 112, normalized size = 0.82 \[ -\frac {43758 \, b^{10} x^{5} + 388960 \, a b^{9} x^{\frac {9}{2}} + 1575288 \, a^{2} b^{8} x^{4} + 3818880 \, a^{3} b^{7} x^{\frac {7}{2}} + 6126120 \, a^{4} b^{6} x^{3} + 6785856 \, a^{5} b^{5} x^{\frac {5}{2}} + 5250960 \, a^{6} b^{4} x^{2} + 2800512 \, a^{7} b^{3} x^{\frac {3}{2}} + 984555 \, a^{8} b^{2} x + 205920 \, a^{9} b \sqrt {x} + 19448 \, a^{10}}{175032 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 112, normalized size = 0.82 \[ -\frac {\frac {a^{10}}{9}+\frac {b^{10}\,x^5}{4}+\frac {45\,a^8\,b^2\,x}{8}+\frac {20\,a^9\,b\,\sqrt {x}}{17}+\frac {20\,a\,b^9\,x^{9/2}}{9}+30\,a^6\,b^4\,x^2+35\,a^4\,b^6\,x^3+9\,a^2\,b^8\,x^4+16\,a^7\,b^3\,x^{3/2}+\frac {504\,a^5\,b^5\,x^{5/2}}{13}+\frac {240\,a^3\,b^7\,x^{7/2}}{11}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 9.42, size = 138, normalized size = 1.01 \[ - \frac {a^{10}}{9 x^{9}} - \frac {20 a^{9} b}{17 x^{\frac {17}{2}}} - \frac {45 a^{8} b^{2}}{8 x^{8}} - \frac {16 a^{7} b^{3}}{x^{\frac {15}{2}}} - \frac {30 a^{6} b^{4}}{x^{7}} - \frac {504 a^{5} b^{5}}{13 x^{\frac {13}{2}}} - \frac {35 a^{4} b^{6}}{x^{6}} - \frac {240 a^{3} b^{7}}{11 x^{\frac {11}{2}}} - \frac {9 a^{2} b^{8}}{x^{5}} - \frac {20 a b^{9}}{9 x^{\frac {9}{2}}} - \frac {b^{10}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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