Optimal. Leaf size=47 \[ -\frac{2 a^2 b}{3 x^{9/2}}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0197708, antiderivative size = 47, 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} \[ -\frac{2 a^2 b}{3 x^{9/2}}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt{x}\right )^3}{x^6} \, dx &=2 \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^{11}} \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (\frac{a^3}{x^{11}}+\frac{3 a^2 b}{x^{10}}+\frac{3 a b^2}{x^9}+\frac{b^3}{x^8}\right ) \, dx,x,\sqrt{x}\right )\\ &=-\frac{a^3}{5 x^5}-\frac{2 a^2 b}{3 x^{9/2}}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}}\\ \end{align*}
Mathematica [A] time = 0.0165871, size = 41, normalized size = 0.87 \[ -\frac{280 a^2 b \sqrt{x}+84 a^3+315 a b^2 x+120 b^3 x^{3/2}}{420 x^5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{5\,{x}^{5}}}-{\frac{2\,b{a}^{2}}{3}{x}^{-{\frac{9}{2}}}}-{\frac{3\,{b}^{2}a}{4\,{x}^{4}}}-{\frac{2\,{b}^{3}}{7}{x}^{-{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.977384, size = 47, normalized size = 1. \begin{align*} -\frac{120 \, b^{3} x^{\frac{3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt{x} + 84 \, a^{3}}{420 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48485, size = 92, normalized size = 1.96 \begin{align*} -\frac{315 \, a b^{2} x + 84 \, a^{3} + 40 \,{\left (3 \, b^{3} x + 7 \, a^{2} b\right )} \sqrt{x}}{420 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 2.953, size = 46, normalized size = 0.98 \begin{align*} - \frac{a^{3}}{5 x^{5}} - \frac{2 a^{2} b}{3 x^{\frac{9}{2}}} - \frac{3 a b^{2}}{4 x^{4}} - \frac{2 b^{3}}{7 x^{\frac{7}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11883, size = 47, normalized size = 1. \begin{align*} -\frac{120 \, b^{3} x^{\frac{3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt{x} + 84 \, a^{3}}{420 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]