Optimal. Leaf size=34 \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{7 x^{7/3}}-\frac{3 b^2}{8 x^{8/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0173652, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {263, 266, 43} \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{7 x^{7/3}}-\frac{3 b^2}{8 x^{8/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 263
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{\sqrt [3]{x}}\right )^2}{x^3} \, dx &=\int \frac{\left (b+a \sqrt [3]{x}\right )^2}{x^{11/3}} \, dx\\ &=3 \operatorname{Subst}\left (\int \frac{(b+a x)^2}{x^9} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{b^2}{x^9}+\frac{2 a b}{x^8}+\frac{a^2}{x^7}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{3 b^2}{8 x^{8/3}}-\frac{6 a b}{7 x^{7/3}}-\frac{a^2}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0202941, size = 34, normalized size = 1. \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{7 x^{7/3}}-\frac{3 b^2}{8 x^{8/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 25, normalized size = 0.7 \begin{align*} -{\frac{3\,{b}^{2}}{8}{x}^{-{\frac{8}{3}}}}-{\frac{6\,ab}{7}{x}^{-{\frac{7}{3}}}}-{\frac{{a}^{2}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 0.977857, size = 131, normalized size = 3.85 \begin{align*} -\frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{8}}{8 \, b^{6}} + \frac{15 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7} a}{7 \, b^{6}} - \frac{5 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a^{2}}{b^{6}} + \frac{6 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{3}}{b^{6}} - \frac{15 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{4}}{4 \, b^{6}} + \frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{3} a^{5}}{b^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.50993, size = 76, normalized size = 2.24 \begin{align*} -\frac{28 \, a^{2} x + 48 \, a b x^{\frac{2}{3}} + 21 \, b^{2} x^{\frac{1}{3}}}{56 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.49017, size = 32, normalized size = 0.94 \begin{align*} - \frac{a^{2}}{2 x^{2}} - \frac{6 a b}{7 x^{\frac{7}{3}}} - \frac{3 b^{2}}{8 x^{\frac{8}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17628, size = 35, normalized size = 1.03 \begin{align*} -\frac{28 \, a^{2} x^{\frac{2}{3}} + 48 \, a b x^{\frac{1}{3}} + 21 \, b^{2}}{56 \, x^{\frac{8}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]