Optimal. Leaf size=31 \[ -\frac {a B+A b}{x}-\frac {a A}{4 x^4}+\frac {1}{2} b B x^2 \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {448} \begin {gather*} -\frac {a B+A b}{x}-\frac {a A}{4 x^4}+\frac {1}{2} b B x^2 \end {gather*}
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^5} \, dx &=\int \left (\frac {a A}{x^5}+\frac {A b+a B}{x^2}+b B x\right ) \, dx\\ &=-\frac {a A}{4 x^4}-\frac {A b+a B}{x}+\frac {1}{2} b B x^2\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 32, normalized size = 1.03 \begin {gather*} \frac {-a B-A b}{x}-\frac {a A}{4 x^4}+\frac {1}{2} b B x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right ) \left (A+B x^3\right )}{x^5} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.29, size = 29, normalized size = 0.94 \begin {gather*} \frac {2 \, B b x^{6} - 4 \, {\left (B a + A b\right )} x^{3} - A a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 31, normalized size = 1.00 \begin {gather*} \frac {1}{2} \, B b x^{2} - \frac {4 \, B a x^{3} + 4 \, A b x^{3} + A a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 28, normalized size = 0.90 \begin {gather*} \frac {B b \,x^{2}}{2}-\frac {A b +B a}{x}-\frac {A a}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.63, size = 29, normalized size = 0.94 \begin {gather*} \frac {1}{2} \, B b x^{2} - \frac {4 \, {\left (B a + A b\right )} x^{3} + A a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 29, normalized size = 0.94 \begin {gather*} \frac {B\,b\,x^2}{2}-\frac {\left (A\,b+B\,a\right )\,x^3+\frac {A\,a}{4}}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.25, size = 31, normalized size = 1.00 \begin {gather*} \frac {B b x^{2}}{2} + \frac {- A a + x^{3} \left (- 4 A b - 4 B a\right )}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________