Optimal. Leaf size=30 \[ -\frac {b^2}{7 x^7}-\frac {2 b c}{5 x^5}-\frac {c^2}{3 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1598, 276}
\begin {gather*} -\frac {b^2}{7 x^7}-\frac {2 b c}{5 x^5}-\frac {c^2}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 276
Rule 1598
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^2}{x^{12}} \, dx &=\int \frac {\left (b+c x^2\right )^2}{x^8} \, dx\\ &=\int \left (\frac {b^2}{x^8}+\frac {2 b c}{x^6}+\frac {c^2}{x^4}\right ) \, dx\\ &=-\frac {b^2}{7 x^7}-\frac {2 b c}{5 x^5}-\frac {c^2}{3 x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -\frac {b^2}{7 x^7}-\frac {2 b c}{5 x^5}-\frac {c^2}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 25, normalized size = 0.83
method | result | size |
default | \(-\frac {b^{2}}{7 x^{7}}-\frac {2 b c}{5 x^{5}}-\frac {c^{2}}{3 x^{3}}\) | \(25\) |
risch | \(\frac {-\frac {1}{3} c^{2} x^{4}-\frac {2}{5} b c \,x^{2}-\frac {1}{7} b^{2}}{x^{7}}\) | \(26\) |
gosper | \(-\frac {35 c^{2} x^{4}+42 b c \,x^{2}+15 b^{2}}{105 x^{7}}\) | \(27\) |
norman | \(\frac {-\frac {1}{7} b^{2} x^{4}-\frac {1}{3} c^{2} x^{8}-\frac {2}{5} b c \,x^{6}}{x^{11}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 26, normalized size = 0.87 \begin {gather*} -\frac {35 \, c^{2} x^{4} + 42 \, b c x^{2} + 15 \, b^{2}}{105 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 26, normalized size = 0.87 \begin {gather*} -\frac {35 \, c^{2} x^{4} + 42 \, b c x^{2} + 15 \, b^{2}}{105 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 27, normalized size = 0.90 \begin {gather*} \frac {- 15 b^{2} - 42 b c x^{2} - 35 c^{2} x^{4}}{105 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 3.82, size = 26, normalized size = 0.87 \begin {gather*} -\frac {35 \, c^{2} x^{4} + 42 \, b c x^{2} + 15 \, b^{2}}{105 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 26, normalized size = 0.87 \begin {gather*} -\frac {\frac {b^2}{7}+\frac {2\,b\,c\,x^2}{5}+\frac {c^2\,x^4}{3}}{x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________