Optimal. Leaf size=34 \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.014822, antiderivative size = 34, 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} \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^2}{x^3} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x^7} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^2}{x^7}+\frac{2 a b}{x^6}+\frac{b^2}{x^5}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}}\\ \end{align*}
Mathematica [A] time = 0.012257, size = 34, normalized size = 1. \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 25, normalized size = 0.7 \begin{align*} -{\frac{{a}^{2}}{2\,{x}^{2}}}-{\frac{6\,ab}{5}{x}^{-{\frac{5}{3}}}}-{\frac{3\,{b}^{2}}{4}{x}^{-{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.968705, size = 35, normalized size = 1.03 \begin{align*} -\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44383, size = 73, normalized size = 2.15 \begin{align*} -\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.37497, size = 32, normalized size = 0.94 \begin{align*} - \frac{a^{2}}{2 x^{2}} - \frac{6 a b}{5 x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 x^{\frac{4}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13355, size = 35, normalized size = 1.03 \begin{align*} -\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]