Optimal. Leaf size=131 \[ -\frac {a^{10}}{3 x^3}-\frac {15 a^9 b}{4 x^{8/3}}-\frac {135 a^8 b^2}{7 x^{7/3}}-\frac {60 a^7 b^3}{x^2}-\frac {126 a^6 b^4}{x^{5/3}}-\frac {189 a^5 b^5}{x^{4/3}}-\frac {210 a^4 b^6}{x}-\frac {180 a^3 b^7}{x^{2/3}}-\frac {135 a^2 b^8}{\sqrt [3]{x}}+10 a b^9 \log (x)+3 b^{10} \sqrt [3]{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 131, 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} \[ -\frac {135 a^8 b^2}{7 x^{7/3}}-\frac {60 a^7 b^3}{x^2}-\frac {126 a^6 b^4}{x^{5/3}}-\frac {189 a^5 b^5}{x^{4/3}}-\frac {180 a^3 b^7}{x^{2/3}}-\frac {210 a^4 b^6}{x}-\frac {135 a^2 b^8}{\sqrt [3]{x}}-\frac {15 a^9 b}{4 x^{8/3}}-\frac {a^{10}}{3 x^3}+10 a b^9 \log (x)+3 b^{10} \sqrt [3]{x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^{10}}{x^4} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{10}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (b^{10}+\frac {a^{10}}{x^{10}}+\frac {10 a^9 b}{x^9}+\frac {45 a^8 b^2}{x^8}+\frac {120 a^7 b^3}{x^7}+\frac {210 a^6 b^4}{x^6}+\frac {252 a^5 b^5}{x^5}+\frac {210 a^4 b^6}{x^4}+\frac {120 a^3 b^7}{x^3}+\frac {45 a^2 b^8}{x^2}+\frac {10 a b^9}{x}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^{10}}{3 x^3}-\frac {15 a^9 b}{4 x^{8/3}}-\frac {135 a^8 b^2}{7 x^{7/3}}-\frac {60 a^7 b^3}{x^2}-\frac {126 a^6 b^4}{x^{5/3}}-\frac {189 a^5 b^5}{x^{4/3}}-\frac {210 a^4 b^6}{x}-\frac {180 a^3 b^7}{x^{2/3}}-\frac {135 a^2 b^8}{\sqrt [3]{x}}+3 b^{10} \sqrt [3]{x}+10 a b^9 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.08, size = 131, normalized size = 1.00 \[ -\frac {a^{10}}{3 x^3}-\frac {15 a^9 b}{4 x^{8/3}}-\frac {135 a^8 b^2}{7 x^{7/3}}-\frac {60 a^7 b^3}{x^2}-\frac {126 a^6 b^4}{x^{5/3}}-\frac {189 a^5 b^5}{x^{4/3}}-\frac {210 a^4 b^6}{x}-\frac {180 a^3 b^7}{x^{2/3}}-\frac {135 a^2 b^8}{\sqrt [3]{x}}+10 a b^9 \log (x)+3 b^{10} \sqrt [3]{x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.87, size = 118, normalized size = 0.90 \[ \frac {2520 \, a b^{9} x^{3} \log \left (x^{\frac {1}{3}}\right ) - 17640 \, a^{4} b^{6} x^{2} - 5040 \, a^{7} b^{3} x - 28 \, a^{10} - 324 \, {\left (35 \, a^{2} b^{8} x^{2} + 49 \, a^{5} b^{5} x + 5 \, a^{8} b^{2}\right )} x^{\frac {2}{3}} + 63 \, {\left (4 \, b^{10} x^{3} - 240 \, a^{3} b^{7} x^{2} - 168 \, a^{6} b^{4} x - 5 \, a^{9} b\right )} x^{\frac {1}{3}}}{84 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 113, normalized size = 0.86 \[ 10 \, a b^{9} \log \left ({\left | x \right |}\right ) + 3 \, b^{10} x^{\frac {1}{3}} - \frac {11340 \, a^{2} b^{8} x^{\frac {8}{3}} + 15120 \, a^{3} b^{7} x^{\frac {7}{3}} + 17640 \, a^{4} b^{6} x^{2} + 15876 \, a^{5} b^{5} x^{\frac {5}{3}} + 10584 \, a^{6} b^{4} x^{\frac {4}{3}} + 5040 \, a^{7} b^{3} x + 1620 \, a^{8} b^{2} x^{\frac {2}{3}} + 315 \, a^{9} b x^{\frac {1}{3}} + 28 \, a^{10}}{84 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 112, normalized size = 0.85 \[ 10 a \,b^{9} \ln \relax (x )+3 b^{10} x^{\frac {1}{3}}-\frac {135 a^{2} b^{8}}{x^{\frac {1}{3}}}-\frac {180 a^{3} b^{7}}{x^{\frac {2}{3}}}-\frac {210 a^{4} b^{6}}{x}-\frac {189 a^{5} b^{5}}{x^{\frac {4}{3}}}-\frac {126 a^{6} b^{4}}{x^{\frac {5}{3}}}-\frac {60 a^{7} b^{3}}{x^{2}}-\frac {135 a^{8} b^{2}}{7 x^{\frac {7}{3}}}-\frac {15 a^{9} b}{4 x^{\frac {8}{3}}}-\frac {a^{10}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.92, size = 112, normalized size = 0.85 \[ 10 \, a b^{9} \log \relax (x) + 3 \, b^{10} x^{\frac {1}{3}} - \frac {11340 \, a^{2} b^{8} x^{\frac {8}{3}} + 15120 \, a^{3} b^{7} x^{\frac {7}{3}} + 17640 \, a^{4} b^{6} x^{2} + 15876 \, a^{5} b^{5} x^{\frac {5}{3}} + 10584 \, a^{6} b^{4} x^{\frac {4}{3}} + 5040 \, a^{7} b^{3} x + 1620 \, a^{8} b^{2} x^{\frac {2}{3}} + 315 \, a^{9} b x^{\frac {1}{3}} + 28 \, a^{10}}{84 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.16, size = 113, normalized size = 0.86 \[ 3\,b^{10}\,x^{1/3}-\frac {a^{10}}{3\,x^3}-\frac {15\,a^9\,b}{4\,x^{8/3}}-\frac {210\,a^4\,b^6}{x}-\frac {60\,a^7\,b^3}{x^2}-\frac {135\,a^2\,b^8}{x^{1/3}}-\frac {180\,a^3\,b^7}{x^{2/3}}-\frac {189\,a^5\,b^5}{x^{4/3}}-\frac {126\,a^6\,b^4}{x^{5/3}}-\frac {135\,a^8\,b^2}{7\,x^{7/3}}+30\,a\,b^9\,\ln \left (x^{1/3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 2.42, size = 133, normalized size = 1.02 \[ - \frac {a^{10}}{3 x^{3}} - \frac {15 a^{9} b}{4 x^{\frac {8}{3}}} - \frac {135 a^{8} b^{2}}{7 x^{\frac {7}{3}}} - \frac {60 a^{7} b^{3}}{x^{2}} - \frac {126 a^{6} b^{4}}{x^{\frac {5}{3}}} - \frac {189 a^{5} b^{5}}{x^{\frac {4}{3}}} - \frac {210 a^{4} b^{6}}{x} - \frac {180 a^{3} b^{7}}{x^{\frac {2}{3}}} - \frac {135 a^{2} b^{8}}{\sqrt [3]{x}} + 10 a b^{9} \log {\relax (x )} + 3 b^{10} \sqrt [3]{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________