Optimal. Leaf size=25 \[ \frac{2 \left (a x^4+b x^7\right )^{3/2}}{9 b x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0078477, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {1979, 2000} \[ \frac{2 \left (a x^4+b x^7\right )^{3/2}}{9 b x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1979
Rule 2000
Rubi steps
\begin{align*} \int \sqrt{x^4 \left (a+b x^3\right )} \, dx &=\int \sqrt{a x^4+b x^7} \, dx\\ &=\frac{2 \left (a x^4+b x^7\right )^{3/2}}{9 b x^6}\\ \end{align*}
Mathematica [A] time = 0.010894, size = 25, normalized size = 1. \[ \frac{2 \left (x^4 \left (a+b x^3\right )\right )^{3/2}}{9 b x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 29, normalized size = 1.2 \begin{align*}{\frac{2\,b{x}^{3}+2\,a}{9\,b{x}^{2}}\sqrt{{x}^{4} \left ( b{x}^{3}+a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.1652, size = 19, normalized size = 0.76 \begin{align*} \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.918432, size = 61, normalized size = 2.44 \begin{align*} \frac{2 \, \sqrt{b x^{7} + a x^{4}}{\left (b x^{3} + a\right )}}{9 \, b x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.24237, size = 19, normalized size = 0.76 \begin{align*} \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]