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 = {1598, 270}
\begin {gather*} -\frac {\left (b+c x^2\right )^3}{6 b x^6} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rule 1598
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 \begin {gather*} -\frac {b^2}{6 x^6}-\frac {b c}{2 x^4}-\frac {c^2}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 25, normalized size = 1.32
method | result | size |
gosper | \(-\frac {3 c^{2} x^{4}+3 b c \,x^{2}+b^{2}}{6 x^{6}}\) | \(25\) |
default | \(-\frac {b c}{2 x^{4}}-\frac {c^{2}}{2 x^{2}}-\frac {b^{2}}{6 x^{6}}\) | \(25\) |
risch | \(\frac {-\frac {1}{2} c^{2} x^{4}-\frac {1}{2} b c \,x^{2}-\frac {1}{6} b^{2}}{x^{6}}\) | \(26\) |
norman | \(\frac {-\frac {1}{6} b^{2} x^{4}-\frac {1}{2} c^{2} x^{8}-\frac {1}{2} b c \,x^{6}}{x^{10}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 24, normalized size = 1.26 \begin {gather*} -\frac {3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 24, normalized size = 1.26 \begin {gather*} -\frac {3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 26, normalized size = 1.37 \begin {gather*} \frac {- b^{2} - 3 b c x^{2} - 3 c^{2} x^{4}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.49, size = 24, normalized size = 1.26 \begin {gather*} -\frac {3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 26, normalized size = 1.37 \begin {gather*} -\frac {\frac {b^2}{6}+\frac {b\,c\,x^2}{2}+\frac {c^2\,x^4}{2}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________