Optimal. Leaf size=41 \[ -\frac {c^6 (a-b x)^7}{8 x^8}-\frac {9 b c^6 (a-b x)^7}{56 a x^7} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {79, 37}
\begin {gather*} -\frac {c^6 (a-b x)^7}{8 x^8}-\frac {9 b c^6 (a-b x)^7}{56 a x^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rule 79
Rubi steps
\begin {align*} \int \frac {(a+b x) (a c-b c x)^6}{x^9} \, dx &=-\frac {c^6 (a-b x)^7}{8 x^8}+\frac {1}{8} (9 b) \int \frac {(a c-b c x)^6}{x^8} \, dx\\ &=-\frac {c^6 (a-b x)^7}{8 x^8}-\frac {9 b c^6 (a-b x)^7}{56 a x^7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(112\) vs. \(2(41)=82\).
time = 0.01, size = 112, normalized size = 2.73 \begin {gather*} -\frac {a^7 c^6}{8 x^8}+\frac {5 a^6 b c^6}{7 x^7}-\frac {3 a^5 b^2 c^6}{2 x^6}+\frac {a^4 b^3 c^6}{x^5}+\frac {5 a^3 b^4 c^6}{4 x^4}-\frac {3 a^2 b^5 c^6}{x^3}+\frac {5 a b^6 c^6}{2 x^2}-\frac {b^7 c^6}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(82\) vs.
\(2(37)=74\).
time = 0.06, size = 83, normalized size = 2.02
method | result | size |
gosper | \(-\frac {c^{6} \left (56 b^{7} x^{7}-140 a \,b^{6} x^{6}+168 a^{2} b^{5} x^{5}-70 a^{3} b^{4} x^{4}-56 a^{4} b^{3} x^{3}+84 a^{5} b^{2} x^{2}-40 a^{6} b x +7 a^{7}\right )}{56 x^{8}}\) | \(83\) |
default | \(c^{6} \left (-\frac {b^{7}}{x}+\frac {a^{4} b^{3}}{x^{5}}+\frac {5 a^{3} b^{4}}{4 x^{4}}-\frac {3 a^{5} b^{2}}{2 x^{6}}+\frac {5 a \,b^{6}}{2 x^{2}}-\frac {3 a^{2} b^{5}}{x^{3}}-\frac {a^{7}}{8 x^{8}}+\frac {5 a^{6} b}{7 x^{7}}\right )\) | \(83\) |
norman | \(\frac {a^{4} b^{3} c^{6} x^{3}-\frac {1}{8} a^{7} c^{6}-b^{7} c^{6} x^{7}+\frac {5}{2} a \,b^{6} c^{6} x^{6}-3 a^{2} b^{5} c^{6} x^{5}+\frac {5}{4} a^{3} b^{4} c^{6} x^{4}-\frac {3}{2} a^{5} b^{2} c^{6} x^{2}+\frac {5}{7} a^{6} b \,c^{6} x}{x^{8}}\) | \(102\) |
risch | \(\frac {a^{4} b^{3} c^{6} x^{3}-\frac {1}{8} a^{7} c^{6}-b^{7} c^{6} x^{7}+\frac {5}{2} a \,b^{6} c^{6} x^{6}-3 a^{2} b^{5} c^{6} x^{5}+\frac {5}{4} a^{3} b^{4} c^{6} x^{4}-\frac {3}{2} a^{5} b^{2} c^{6} x^{2}+\frac {5}{7} a^{6} b \,c^{6} x}{x^{8}}\) | \(102\) |
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. 103 vs.
\(2 (39) = 78\).
time = 0.28, size = 103, normalized size = 2.51 \begin {gather*} -\frac {56 \, b^{7} c^{6} x^{7} - 140 \, a b^{6} c^{6} x^{6} + 168 \, a^{2} b^{5} c^{6} x^{5} - 70 \, a^{3} b^{4} c^{6} x^{4} - 56 \, a^{4} b^{3} c^{6} x^{3} + 84 \, a^{5} b^{2} c^{6} x^{2} - 40 \, a^{6} b c^{6} x + 7 \, a^{7} c^{6}}{56 \, x^{8}} \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. 103 vs.
\(2 (39) = 78\).
time = 1.17, size = 103, normalized size = 2.51 \begin {gather*} -\frac {56 \, b^{7} c^{6} x^{7} - 140 \, a b^{6} c^{6} x^{6} + 168 \, a^{2} b^{5} c^{6} x^{5} - 70 \, a^{3} b^{4} c^{6} x^{4} - 56 \, a^{4} b^{3} c^{6} x^{3} + 84 \, a^{5} b^{2} c^{6} x^{2} - 40 \, a^{6} b c^{6} x + 7 \, a^{7} c^{6}}{56 \, x^{8}} \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. 110 vs.
\(2 (36) = 72\).
time = 0.30, size = 110, normalized size = 2.68 \begin {gather*} \frac {- 7 a^{7} c^{6} + 40 a^{6} b c^{6} x - 84 a^{5} b^{2} c^{6} x^{2} + 56 a^{4} b^{3} c^{6} x^{3} + 70 a^{3} b^{4} c^{6} x^{4} - 168 a^{2} b^{5} c^{6} x^{5} + 140 a b^{6} c^{6} x^{6} - 56 b^{7} c^{6} x^{7}}{56 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 103 vs.
\(2 (39) = 78\).
time = 0.91, size = 103, normalized size = 2.51 \begin {gather*} -\frac {56 \, b^{7} c^{6} x^{7} - 140 \, a b^{6} c^{6} x^{6} + 168 \, a^{2} b^{5} c^{6} x^{5} - 70 \, a^{3} b^{4} c^{6} x^{4} - 56 \, a^{4} b^{3} c^{6} x^{3} + 84 \, a^{5} b^{2} c^{6} x^{2} - 40 \, a^{6} b c^{6} x + 7 \, a^{7} c^{6}}{56 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.07, size = 102, normalized size = 2.49 \begin {gather*} -\frac {\frac {a^7\,c^6}{8}-\frac {5\,a^6\,b\,c^6\,x}{7}+\frac {3\,a^5\,b^2\,c^6\,x^2}{2}-a^4\,b^3\,c^6\,x^3-\frac {5\,a^3\,b^4\,c^6\,x^4}{4}+3\,a^2\,b^5\,c^6\,x^5-\frac {5\,a\,b^6\,c^6\,x^6}{2}+b^7\,c^6\,x^7}{x^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________