Optimal. Leaf size=125 \[ 378 a^5 b^5 x^{2/3}+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+630 a^6 b^4 \sqrt [3]{x}+210 a^4 b^6 x+120 a^7 b^3 \log (x)-\frac{15 a^9 b}{x^{2/3}}-\frac{a^{10}}{x}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0706347, antiderivative size = 125, normalized size of antiderivative = 1., 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} \[ 378 a^5 b^5 x^{2/3}+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+630 a^6 b^4 \sqrt [3]{x}+210 a^4 b^6 x+120 a^7 b^3 \log (x)-\frac{15 a^9 b}{x^{2/3}}-\frac{a^{10}}{x}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^{10}}{x^2} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^{10}}{x^4} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (210 a^6 b^4+\frac{a^{10}}{x^4}+\frac{10 a^9 b}{x^3}+\frac{45 a^8 b^2}{x^2}+\frac{120 a^7 b^3}{x}+252 a^5 b^5 x+210 a^4 b^6 x^2+120 a^3 b^7 x^3+45 a^2 b^8 x^4+10 a b^9 x^5+b^{10} x^6\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^{10}}{x}-\frac{15 a^9 b}{x^{2/3}}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3}+120 a^7 b^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0612866, size = 125, normalized size = 1. \[ 378 a^5 b^5 x^{2/3}+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+630 a^6 b^4 \sqrt [3]{x}+210 a^4 b^6 x+120 a^7 b^3 \log (x)-\frac{15 a^9 b}{x^{2/3}}-\frac{a^{10}}{x}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.008, size = 110, normalized size = 0.9 \begin{align*} -{\frac{{a}^{10}}{x}}-15\,{\frac{{a}^{9}b}{{x}^{2/3}}}-135\,{\frac{{a}^{8}{b}^{2}}{\sqrt [3]{x}}}+630\,{a}^{6}{b}^{4}\sqrt [3]{x}+378\,{a}^{5}{b}^{5}{x}^{2/3}+210\,{a}^{4}{b}^{6}x+90\,{a}^{3}{b}^{7}{x}^{4/3}+27\,{a}^{2}{b}^{8}{x}^{5/3}+5\,a{b}^{9}{x}^{2}+{\frac{3\,{b}^{10}}{7}{x}^{{\frac{7}{3}}}}+120\,{a}^{7}{b}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.996783, size = 149, normalized size = 1.19 \begin{align*} \frac{3}{7} \, b^{10} x^{\frac{7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac{5}{3}} + 90 \, a^{3} b^{7} x^{\frac{4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3} \log \left (x\right ) + 378 \, a^{5} b^{5} x^{\frac{2}{3}} + 630 \, a^{6} b^{4} x^{\frac{1}{3}} - \frac{135 \, a^{8} b^{2} x^{\frac{2}{3}} + 15 \, a^{9} b x^{\frac{1}{3}} + a^{10}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.53582, size = 275, normalized size = 2.2 \begin{align*} \frac{35 \, a b^{9} x^{3} + 1470 \, a^{4} b^{6} x^{2} + 2520 \, a^{7} b^{3} x \log \left (x^{\frac{1}{3}}\right ) - 7 \, a^{10} + 189 \,{\left (a^{2} b^{8} x^{2} + 14 \, a^{5} b^{5} x - 5 \, a^{8} b^{2}\right )} x^{\frac{2}{3}} + 3 \,{\left (b^{10} x^{3} + 210 \, a^{3} b^{7} x^{2} + 1470 \, a^{6} b^{4} x - 35 \, a^{9} b\right )} x^{\frac{1}{3}}}{7 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 14.9041, size = 131, normalized size = 1.05 \begin{align*} - \frac{a^{10}}{x} - \frac{15 a^{9} b}{x^{\frac{2}{3}}} - \frac{135 a^{8} b^{2}}{\sqrt [3]{x}} + 360 a^{7} b^{3} \log{\left (\sqrt [3]{x} \right )} + 630 a^{6} b^{4} \sqrt [3]{x} + 378 a^{5} b^{5} x^{\frac{2}{3}} + 210 a^{4} b^{6} x + 90 a^{3} b^{7} x^{\frac{4}{3}} + 27 a^{2} b^{8} x^{\frac{5}{3}} + 5 a b^{9} x^{2} + \frac{3 b^{10} x^{\frac{7}{3}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20909, size = 150, normalized size = 1.2 \begin{align*} \frac{3}{7} \, b^{10} x^{\frac{7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac{5}{3}} + 90 \, a^{3} b^{7} x^{\frac{4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3} \log \left ({\left | x \right |}\right ) + 378 \, a^{5} b^{5} x^{\frac{2}{3}} + 630 \, a^{6} b^{4} x^{\frac{1}{3}} - \frac{135 \, a^{8} b^{2} x^{\frac{2}{3}} + 15 \, a^{9} b x^{\frac{1}{3}} + a^{10}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]