Optimal. Leaf size=37 \[ 2 \sqrt{x} (a B+A b)-\frac{2 a A}{5 x^{5/2}}+\frac{2}{7} b B x^{7/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0161729, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ 2 \sqrt{x} (a B+A b)-\frac{2 a A}{5 x^{5/2}}+\frac{2}{7} b B x^{7/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^{7/2}} \, dx &=\int \left (\frac{a A}{x^{7/2}}+\frac{A b+a B}{\sqrt{x}}+b B x^{5/2}\right ) \, dx\\ &=-\frac{2 a A}{5 x^{5/2}}+2 (A b+a B) \sqrt{x}+\frac{2}{7} b B x^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0110783, size = 36, normalized size = 0.97 \[ \frac{2 \left (5 b x^3 \left (7 A+B x^3\right )-7 a \left (A-5 B x^3\right )\right )}{35 x^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 32, normalized size = 0.9 \begin{align*} -{\frac{-10\,bB{x}^{6}-70\,A{x}^{3}b-70\,B{x}^{3}a+14\,Aa}{35}{x}^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.983294, size = 36, normalized size = 0.97 \begin{align*} \frac{2}{7} \, B b x^{\frac{7}{2}} + 2 \,{\left (B a + A b\right )} \sqrt{x} - \frac{2 \, A a}{5 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.74647, size = 74, normalized size = 2. \begin{align*} \frac{2 \,{\left (5 \, B b x^{6} + 35 \,{\left (B a + A b\right )} x^{3} - 7 \, A a\right )}}{35 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 4.23594, size = 42, normalized size = 1.14 \begin{align*} - \frac{2 A a}{5 x^{\frac{5}{2}}} + 2 A b \sqrt{x} + 2 B a \sqrt{x} + \frac{2 B b x^{\frac{7}{2}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10656, size = 39, normalized size = 1.05 \begin{align*} \frac{2}{7} \, B b x^{\frac{7}{2}} + 2 \, B a \sqrt{x} + 2 \, A b \sqrt{x} - \frac{2 \, A a}{5 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]