Optimal. Leaf size=19 \[ -\frac {\left (a+b x^3\right )^4}{12 a x^{12}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {264} \[ -\frac {\left (a+b x^3\right )^4}{12 a x^{12}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^{13}} \, dx &=-\frac {\left (a+b x^3\right )^4}{12 a x^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.01, size = 43, normalized size = 2.26 \[ -\frac {a^3}{12 x^{12}}-\frac {a^2 b}{3 x^9}-\frac {a b^2}{2 x^6}-\frac {b^3}{3 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.77, size = 35, normalized size = 1.84 \[ -\frac {4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.15, size = 35, normalized size = 1.84 \[ -\frac {4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.00, size = 36, normalized size = 1.89 \[ -\frac {b^{3}}{3 x^{3}}-\frac {a \,b^{2}}{2 x^{6}}-\frac {a^{2} b}{3 x^{9}}-\frac {a^{3}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.35, size = 35, normalized size = 1.84 \[ -\frac {4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 37, normalized size = 1.95 \[ -\frac {\frac {a^3}{12}+\frac {a^2\,b\,x^3}{3}+\frac {a\,b^2\,x^6}{2}+\frac {b^3\,x^9}{3}}{x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.38, size = 37, normalized size = 1.95 \[ \frac {- a^{3} - 4 a^{2} b x^{3} - 6 a b^{2} x^{6} - 4 b^{3} x^{9}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________