Optimal. Leaf size=19 \[ -\frac {\left (b+c x^2\right )^3}{6 b x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 264} \[ -\frac {\left (b+c x^2\right )^3}{6 b x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^2}{x^{11}} \, dx &=\int \frac {\left (b+c x^2\right )^2}{x^7} \, dx\\ &=-\frac {\left (b+c x^2\right )^3}{6 b x^6}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 30, normalized size = 1.58 \[ -\frac {b^2}{6 x^6}-\frac {b c}{2 x^4}-\frac {c^2}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.69, size = 24, normalized size = 1.26 \[ -\frac {3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 24, normalized size = 1.26 \[ -\frac {3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 25, normalized size = 1.32 \[ -\frac {c^{2}}{2 x^{2}}-\frac {b c}{2 x^{4}}-\frac {b^{2}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.23, size = 24, normalized size = 1.26 \[ -\frac {3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 26, normalized size = 1.37 \[ -\frac {\frac {b^2}{6}+\frac {b\,c\,x^2}{2}+\frac {c^2\,x^4}{2}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.21, size = 26, normalized size = 1.37 \[ \frac {- b^{2} - 3 b c x^{2} - 3 c^{2} x^{4}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________