Optimal. Leaf size=16 \[ -\frac {1}{14 x^{14} \left (b+c x^2\right )^7} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {1598, 457, 75}
\begin {gather*} -\frac {1}{14 x^{14} \left (b+c x^2\right )^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 75
Rule 457
Rule 1598
Rubi steps
\begin {align*} \int \frac {b+2 c x^2}{x^7 \left (b x+c x^3\right )^8} \, dx &=\int \frac {b+2 c x^2}{x^{15} \left (b+c x^2\right )^8} \, dx\\ &=\frac {1}{2} \text {Subst}\left (\int \frac {b+2 c x}{x^8 (b+c x)^8} \, dx,x,x^2\right )\\ &=-\frac {1}{14 x^{14} \left (b+c x^2\right )^7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{14 x^{14} \left (b+c x^2\right )^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(196\) vs.
\(2(14)=28\).
time = 0.21, size = 197, normalized size = 12.31
method | result | size |
gosper | \(-\frac {1}{14 x^{14} \left (c \,x^{2}+b \right )^{7}}\) | \(15\) |
norman | \(-\frac {1}{14 x^{14} \left (c \,x^{2}+b \right )^{7}}\) | \(15\) |
risch | \(-\frac {1}{14 x^{14} \left (c \,x^{2}+b \right )^{7}}\) | \(15\) |
default | \(-\frac {c^{8} \left (-\frac {4 b^{4}}{c \left (c \,x^{2}+b \right )^{5}}-\frac {30 b^{2}}{c \left (c \,x^{2}+b \right )^{3}}-\frac {132}{c \left (c \,x^{2}+b \right )}-\frac {66 b}{c \left (c \,x^{2}+b \right )^{2}}-\frac {b^{6}}{7 c \left (c \,x^{2}+b \right )^{7}}-\frac {b^{5}}{c \left (c \,x^{2}+b \right )^{6}}-\frac {12 b^{3}}{c \left (c \,x^{2}+b \right )^{4}}\right )}{2 b^{13}}-\frac {1}{14 b^{7} x^{14}}-\frac {66 c^{6}}{b^{13} x^{2}}+\frac {33 c^{5}}{b^{12} x^{4}}-\frac {15 c^{4}}{b^{11} x^{6}}+\frac {6 c^{3}}{b^{10} x^{8}}-\frac {2 c^{2}}{b^{9} x^{10}}+\frac {c}{2 b^{8} x^{12}}\) | \(197\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 81 vs.
\(2 (14) = 28\).
time = 0.30, size = 81, normalized size = 5.06 \begin {gather*} -\frac {1}{14 \, {\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 81 vs.
\(2 (14) = 28\).
time = 0.37, size = 81, normalized size = 5.06 \begin {gather*} -\frac {1}{14 \, {\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 87 vs.
\(2 (15) = 30\).
time = 0.70, size = 87, normalized size = 5.44 \begin {gather*} - \frac {1}{14 b^{7} x^{14} + 98 b^{6} c x^{16} + 294 b^{5} c^{2} x^{18} + 490 b^{4} c^{3} x^{20} + 490 b^{3} c^{4} x^{22} + 294 b^{2} c^{5} x^{24} + 98 b c^{6} x^{26} + 14 c^{7} x^{28}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.76, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{14 \, {\left (c x^{4} + b x^{2}\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 2.22, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{14\,x^{14}\,{\left (c\,x^2+b\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________