Optimal. Leaf size=113 \[ \frac {F^{a+\frac {b}{(c+d x)^3}} \left (120 (c+d x)^{15}-120 b (c+d x)^{12} \log (F)+60 b^2 (c+d x)^9 \log ^2(F)-20 b^3 (c+d x)^6 \log ^3(F)+5 b^4 (c+d x)^3 \log ^4(F)-b^5 \log ^5(F)\right )}{3 b^6 d (c+d x)^{15} \log ^6(F)} \]
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Rubi [A]
time = 0.07, antiderivative size = 113, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2249}
\begin {gather*} \frac {F^{a+\frac {b}{(c+d x)^3}} \left (-b^5 \log ^5(F)+5 b^4 \log ^4(F) (c+d x)^3-20 b^3 \log ^3(F) (c+d x)^6+60 b^2 \log ^2(F) (c+d x)^9-120 b \log (F) (c+d x)^{12}+120 (c+d x)^{15}\right )}{3 b^6 d \log ^6(F) (c+d x)^{15}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2249
Rubi steps
\begin {align*} \int \frac {F^{a+\frac {b}{(c+d x)^3}}}{(c+d x)^{19}} \, dx &=\frac {F^a \Gamma \left (6,-\frac {b \log (F)}{(c+d x)^3}\right )}{3 b^6 d \log ^6(F)}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.01, size = 31, normalized size = 0.27 \begin {gather*} \frac {F^a \Gamma \left (6,-\frac {b \log (F)}{(c+d x)^3}\right )}{3 b^6 d \log ^6(F)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(732\) vs.
\(2(111)=222\).
time = 0.11, size = 733, normalized size = 6.49
method | result | size |
risch | \(-\frac {\left (b^{5} \ln \left (F \right )^{5}-120 c^{15}-5040 \ln \left (F \right )^{2} b^{2} c^{3} d^{6} x^{6}+95040 \ln \left (F \right ) b \,c^{7} d^{5} x^{5}-7560 \ln \left (F \right )^{2} b^{2} c^{4} d^{5} x^{5}+59400 \ln \left (F \right ) b \,c^{8} d^{4} x^{4}-7560 \ln \left (F \right )^{2} b^{2} c^{5} d^{4} x^{4}+26400 \ln \left (F \right ) b \,c^{9} d^{3} x^{3}-5040 \ln \left (F \right )^{2} b^{2} c^{6} d^{3} x^{3}+7920 \ln \left (F \right ) b \,c^{10} d^{2} x^{2}-2160 \ln \left (F \right )^{2} b^{2} c^{7} d^{2} x^{2}+1440 \ln \left (F \right ) b \,c^{11} d x -540 \ln \left (F \right )^{2} b^{2} c^{8} d x -15 \ln \left (F \right )^{4} b^{4} c \,d^{2} x^{2}-15 \ln \left (F \right )^{4} b^{4} c^{2} d x +1440 \ln \left (F \right ) b c \,d^{11} x^{11}+7920 \ln \left (F \right ) b \,c^{2} d^{10} x^{10}+26400 \ln \left (F \right ) b \,c^{3} d^{9} x^{9}+59400 \ln \left (F \right ) b \,c^{4} d^{8} x^{8}-540 \ln \left (F \right )^{2} b^{2} c \,d^{8} x^{8}+95040 \ln \left (F \right ) b \,c^{5} d^{7} x^{7}-2160 \ln \left (F \right )^{2} b^{2} c^{2} d^{7} x^{7}+110880 \ln \left (F \right ) b \,c^{6} d^{6} x^{6}+120 c \,d^{5} x^{5} b^{3} \ln \left (F \right )^{3}+300 \ln \left (F \right )^{3} b^{3} c^{2} d^{4} x^{4}+400 \ln \left (F \right )^{3} b^{3} c^{3} d^{3} x^{3}+300 \ln \left (F \right )^{3} b^{3} c^{4} d^{2} x^{2}+120 \ln \left (F \right )^{3} b^{3} c^{5} d x +20 \ln \left (F \right )^{3} b^{3} c^{6}-120 d^{15} x^{15}-1800 c \,d^{14} x^{14}-12600 c^{2} d^{13} x^{13}-54600 c^{3} d^{12} x^{12}-163800 c^{4} d^{11} x^{11}-360360 c^{5} d^{10} x^{10}-600600 c^{6} d^{9} x^{9}-772200 c^{7} d^{8} x^{8}-772200 c^{8} d^{7} x^{7}-600600 c^{9} d^{6} x^{6}-360360 c^{10} d^{5} x^{5}-163800 c^{11} d^{4} x^{4}-54600 c^{12} d^{3} x^{3}-12600 c^{13} d^{2} x^{2}-1800 c^{14} d x +120 \ln \left (F \right ) b \,c^{12}-60 \ln \left (F \right )^{2} b^{2} c^{9}-5 \ln \left (F \right )^{4} b^{4} c^{3}+120 \ln \left (F \right ) b \,d^{12} x^{12}-60 \ln \left (F \right )^{2} b^{2} d^{9} x^{9}-5 \ln \left (F \right )^{4} b^{4} d^{3} x^{3}+20 d^{6} x^{6} b^{3} \ln \left (F \right )^{3}\right ) F^{\frac {a \,d^{3} x^{3}+3 a c \,d^{2} x^{2}+3 a \,c^{2} d x +a \,c^{3}+b}{\left (d x +c \right )^{3}}}}{3 \ln \left (F \right )^{6} b^{6} d \left (d x +c \right )^{15}}\) | \(733\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1085 vs.
\(2 (111) = 222\).
time = 0.32, size = 1085, normalized size = 9.60 \begin {gather*} \frac {{\left (120 \, F^{a} d^{15} x^{15} + 1800 \, F^{a} c d^{14} x^{14} + 12600 \, F^{a} c^{2} d^{13} x^{13} + 120 \, F^{a} c^{15} - 120 \, F^{a} b c^{12} \log \left (F\right ) + 60 \, F^{a} b^{2} c^{9} \log \left (F\right )^{2} + 120 \, {\left (455 \, F^{a} c^{3} d^{12} - F^{a} b d^{12} \log \left (F\right )\right )} x^{12} - 20 \, F^{a} b^{3} c^{6} \log \left (F\right )^{3} + 360 \, {\left (455 \, F^{a} c^{4} d^{11} - 4 \, F^{a} b c d^{11} \log \left (F\right )\right )} x^{11} + 5 \, F^{a} b^{4} c^{3} \log \left (F\right )^{4} + 3960 \, {\left (91 \, F^{a} c^{5} d^{10} - 2 \, F^{a} b c^{2} d^{10} \log \left (F\right )\right )} x^{10} - F^{a} b^{5} \log \left (F\right )^{5} + 60 \, {\left (10010 \, F^{a} c^{6} d^{9} - 440 \, F^{a} b c^{3} d^{9} \log \left (F\right ) + F^{a} b^{2} d^{9} \log \left (F\right )^{2}\right )} x^{9} + 540 \, {\left (1430 \, F^{a} c^{7} d^{8} - 110 \, F^{a} b c^{4} d^{8} \log \left (F\right ) + F^{a} b^{2} c d^{8} \log \left (F\right )^{2}\right )} x^{8} + 1080 \, {\left (715 \, F^{a} c^{8} d^{7} - 88 \, F^{a} b c^{5} d^{7} \log \left (F\right ) + 2 \, F^{a} b^{2} c^{2} d^{7} \log \left (F\right )^{2}\right )} x^{7} + 20 \, {\left (30030 \, F^{a} c^{9} d^{6} - 5544 \, F^{a} b c^{6} d^{6} \log \left (F\right ) + 252 \, F^{a} b^{2} c^{3} d^{6} \log \left (F\right )^{2} - F^{a} b^{3} d^{6} \log \left (F\right )^{3}\right )} x^{6} + 120 \, {\left (3003 \, F^{a} c^{10} d^{5} - 792 \, F^{a} b c^{7} d^{5} \log \left (F\right ) + 63 \, F^{a} b^{2} c^{4} d^{5} \log \left (F\right )^{2} - F^{a} b^{3} c d^{5} \log \left (F\right )^{3}\right )} x^{5} + 60 \, {\left (2730 \, F^{a} c^{11} d^{4} - 990 \, F^{a} b c^{8} d^{4} \log \left (F\right ) + 126 \, F^{a} b^{2} c^{5} d^{4} \log \left (F\right )^{2} - 5 \, F^{a} b^{3} c^{2} d^{4} \log \left (F\right )^{3}\right )} x^{4} + 5 \, {\left (10920 \, F^{a} c^{12} d^{3} - 5280 \, F^{a} b c^{9} d^{3} \log \left (F\right ) + 1008 \, F^{a} b^{2} c^{6} d^{3} \log \left (F\right )^{2} - 80 \, F^{a} b^{3} c^{3} d^{3} \log \left (F\right )^{3} + F^{a} b^{4} d^{3} \log \left (F\right )^{4}\right )} x^{3} + 15 \, {\left (840 \, F^{a} c^{13} d^{2} - 528 \, F^{a} b c^{10} d^{2} \log \left (F\right ) + 144 \, F^{a} b^{2} c^{7} d^{2} \log \left (F\right )^{2} - 20 \, F^{a} b^{3} c^{4} d^{2} \log \left (F\right )^{3} + F^{a} b^{4} c d^{2} \log \left (F\right )^{4}\right )} x^{2} + 15 \, {\left (120 \, F^{a} c^{14} d - 96 \, F^{a} b c^{11} d \log \left (F\right ) + 36 \, F^{a} b^{2} c^{8} d \log \left (F\right )^{2} - 8 \, F^{a} b^{3} c^{5} d \log \left (F\right )^{3} + F^{a} b^{4} c^{2} d \log \left (F\right )^{4}\right )} x\right )} F^{\frac {b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{3 \, {\left (b^{6} d^{16} x^{15} \log \left (F\right )^{6} + 15 \, b^{6} c d^{15} x^{14} \log \left (F\right )^{6} + 105 \, b^{6} c^{2} d^{14} x^{13} \log \left (F\right )^{6} + 455 \, b^{6} c^{3} d^{13} x^{12} \log \left (F\right )^{6} + 1365 \, b^{6} c^{4} d^{12} x^{11} \log \left (F\right )^{6} + 3003 \, b^{6} c^{5} d^{11} x^{10} \log \left (F\right )^{6} + 5005 \, b^{6} c^{6} d^{10} x^{9} \log \left (F\right )^{6} + 6435 \, b^{6} c^{7} d^{9} x^{8} \log \left (F\right )^{6} + 6435 \, b^{6} c^{8} d^{8} x^{7} \log \left (F\right )^{6} + 5005 \, b^{6} c^{9} d^{7} x^{6} \log \left (F\right )^{6} + 3003 \, b^{6} c^{10} d^{6} x^{5} \log \left (F\right )^{6} + 1365 \, b^{6} c^{11} d^{5} x^{4} \log \left (F\right )^{6} + 455 \, b^{6} c^{12} d^{4} x^{3} \log \left (F\right )^{6} + 105 \, b^{6} c^{13} d^{3} x^{2} \log \left (F\right )^{6} + 15 \, b^{6} c^{14} d^{2} x \log \left (F\right )^{6} + b^{6} c^{15} d \log \left (F\right )^{6}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 863 vs.
\(2 (111) = 222\).
time = 0.44, size = 863, normalized size = 7.64 \begin {gather*} \frac {{\left (120 \, d^{15} x^{15} + 1800 \, c d^{14} x^{14} + 12600 \, c^{2} d^{13} x^{13} + 54600 \, c^{3} d^{12} x^{12} + 163800 \, c^{4} d^{11} x^{11} + 360360 \, c^{5} d^{10} x^{10} + 600600 \, c^{6} d^{9} x^{9} + 772200 \, c^{7} d^{8} x^{8} + 772200 \, c^{8} d^{7} x^{7} + 600600 \, c^{9} d^{6} x^{6} + 360360 \, c^{10} d^{5} x^{5} + 163800 \, c^{11} d^{4} x^{4} + 54600 \, c^{12} d^{3} x^{3} + 12600 \, c^{13} d^{2} x^{2} + 1800 \, c^{14} d x + 120 \, c^{15} - b^{5} \log \left (F\right )^{5} + 5 \, {\left (b^{4} d^{3} x^{3} + 3 \, b^{4} c d^{2} x^{2} + 3 \, b^{4} c^{2} d x + b^{4} c^{3}\right )} \log \left (F\right )^{4} - 20 \, {\left (b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + 15 \, b^{3} c^{2} d^{4} x^{4} + 20 \, b^{3} c^{3} d^{3} x^{3} + 15 \, b^{3} c^{4} d^{2} x^{2} + 6 \, b^{3} c^{5} d x + b^{3} c^{6}\right )} \log \left (F\right )^{3} + 60 \, {\left (b^{2} d^{9} x^{9} + 9 \, b^{2} c d^{8} x^{8} + 36 \, b^{2} c^{2} d^{7} x^{7} + 84 \, b^{2} c^{3} d^{6} x^{6} + 126 \, b^{2} c^{4} d^{5} x^{5} + 126 \, b^{2} c^{5} d^{4} x^{4} + 84 \, b^{2} c^{6} d^{3} x^{3} + 36 \, b^{2} c^{7} d^{2} x^{2} + 9 \, b^{2} c^{8} d x + b^{2} c^{9}\right )} \log \left (F\right )^{2} - 120 \, {\left (b d^{12} x^{12} + 12 \, b c d^{11} x^{11} + 66 \, b c^{2} d^{10} x^{10} + 220 \, b c^{3} d^{9} x^{9} + 495 \, b c^{4} d^{8} x^{8} + 792 \, b c^{5} d^{7} x^{7} + 924 \, b c^{6} d^{6} x^{6} + 792 \, b c^{7} d^{5} x^{5} + 495 \, b c^{8} d^{4} x^{4} + 220 \, b c^{9} d^{3} x^{3} + 66 \, b c^{10} d^{2} x^{2} + 12 \, b c^{11} d x + b c^{12}\right )} \log \left (F\right )\right )} F^{\frac {a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{3 \, {\left (b^{6} d^{16} x^{15} + 15 \, b^{6} c d^{15} x^{14} + 105 \, b^{6} c^{2} d^{14} x^{13} + 455 \, b^{6} c^{3} d^{13} x^{12} + 1365 \, b^{6} c^{4} d^{12} x^{11} + 3003 \, b^{6} c^{5} d^{11} x^{10} + 5005 \, b^{6} c^{6} d^{10} x^{9} + 6435 \, b^{6} c^{7} d^{9} x^{8} + 6435 \, b^{6} c^{8} d^{8} x^{7} + 5005 \, b^{6} c^{9} d^{7} x^{6} + 3003 \, b^{6} c^{10} d^{6} x^{5} + 1365 \, b^{6} c^{11} d^{5} x^{4} + 455 \, b^{6} c^{12} d^{4} x^{3} + 105 \, b^{6} c^{13} d^{3} x^{2} + 15 \, b^{6} c^{14} d^{2} x + b^{6} c^{15} d\right )} \log \left (F\right )^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1096 vs.
\(2 (110) = 220\).
time = 50.03, size = 1096, normalized size = 9.70 \begin {gather*} \frac {F^{a + \frac {b}{\left (c + d x\right )^{3}}} \left (- b^{5} \log {\left (F \right )}^{5} + 5 b^{4} c^{3} \log {\left (F \right )}^{4} + 15 b^{4} c^{2} d x \log {\left (F \right )}^{4} + 15 b^{4} c d^{2} x^{2} \log {\left (F \right )}^{4} + 5 b^{4} d^{3} x^{3} \log {\left (F \right )}^{4} - 20 b^{3} c^{6} \log {\left (F \right )}^{3} - 120 b^{3} c^{5} d x \log {\left (F \right )}^{3} - 300 b^{3} c^{4} d^{2} x^{2} \log {\left (F \right )}^{3} - 400 b^{3} c^{3} d^{3} x^{3} \log {\left (F \right )}^{3} - 300 b^{3} c^{2} d^{4} x^{4} \log {\left (F \right )}^{3} - 120 b^{3} c d^{5} x^{5} \log {\left (F \right )}^{3} - 20 b^{3} d^{6} x^{6} \log {\left (F \right )}^{3} + 60 b^{2} c^{9} \log {\left (F \right )}^{2} + 540 b^{2} c^{8} d x \log {\left (F \right )}^{2} + 2160 b^{2} c^{7} d^{2} x^{2} \log {\left (F \right )}^{2} + 5040 b^{2} c^{6} d^{3} x^{3} \log {\left (F \right )}^{2} + 7560 b^{2} c^{5} d^{4} x^{4} \log {\left (F \right )}^{2} + 7560 b^{2} c^{4} d^{5} x^{5} \log {\left (F \right )}^{2} + 5040 b^{2} c^{3} d^{6} x^{6} \log {\left (F \right )}^{2} + 2160 b^{2} c^{2} d^{7} x^{7} \log {\left (F \right )}^{2} + 540 b^{2} c d^{8} x^{8} \log {\left (F \right )}^{2} + 60 b^{2} d^{9} x^{9} \log {\left (F \right )}^{2} - 120 b c^{12} \log {\left (F \right )} - 1440 b c^{11} d x \log {\left (F \right )} - 7920 b c^{10} d^{2} x^{2} \log {\left (F \right )} - 26400 b c^{9} d^{3} x^{3} \log {\left (F \right )} - 59400 b c^{8} d^{4} x^{4} \log {\left (F \right )} - 95040 b c^{7} d^{5} x^{5} \log {\left (F \right )} - 110880 b c^{6} d^{6} x^{6} \log {\left (F \right )} - 95040 b c^{5} d^{7} x^{7} \log {\left (F \right )} - 59400 b c^{4} d^{8} x^{8} \log {\left (F \right )} - 26400 b c^{3} d^{9} x^{9} \log {\left (F \right )} - 7920 b c^{2} d^{10} x^{10} \log {\left (F \right )} - 1440 b c d^{11} x^{11} \log {\left (F \right )} - 120 b d^{12} x^{12} \log {\left (F \right )} + 120 c^{15} + 1800 c^{14} d x + 12600 c^{13} d^{2} x^{2} + 54600 c^{12} d^{3} x^{3} + 163800 c^{11} d^{4} x^{4} + 360360 c^{10} d^{5} x^{5} + 600600 c^{9} d^{6} x^{6} + 772200 c^{8} d^{7} x^{7} + 772200 c^{7} d^{8} x^{8} + 600600 c^{6} d^{9} x^{9} + 360360 c^{5} d^{10} x^{10} + 163800 c^{4} d^{11} x^{11} + 54600 c^{3} d^{12} x^{12} + 12600 c^{2} d^{13} x^{13} + 1800 c d^{14} x^{14} + 120 d^{15} x^{15}\right )}{3 b^{6} c^{15} d \log {\left (F \right )}^{6} + 45 b^{6} c^{14} d^{2} x \log {\left (F \right )}^{6} + 315 b^{6} c^{13} d^{3} x^{2} \log {\left (F \right )}^{6} + 1365 b^{6} c^{12} d^{4} x^{3} \log {\left (F \right )}^{6} + 4095 b^{6} c^{11} d^{5} x^{4} \log {\left (F \right )}^{6} + 9009 b^{6} c^{10} d^{6} x^{5} \log {\left (F \right )}^{6} + 15015 b^{6} c^{9} d^{7} x^{6} \log {\left (F \right )}^{6} + 19305 b^{6} c^{8} d^{8} x^{7} \log {\left (F \right )}^{6} + 19305 b^{6} c^{7} d^{9} x^{8} \log {\left (F \right )}^{6} + 15015 b^{6} c^{6} d^{10} x^{9} \log {\left (F \right )}^{6} + 9009 b^{6} c^{5} d^{11} x^{10} \log {\left (F \right )}^{6} + 4095 b^{6} c^{4} d^{12} x^{11} \log {\left (F \right )}^{6} + 1365 b^{6} c^{3} d^{13} x^{12} \log {\left (F \right )}^{6} + 315 b^{6} c^{2} d^{14} x^{13} \log {\left (F \right )}^{6} + 45 b^{6} c d^{15} x^{14} \log {\left (F \right )}^{6} + 3 b^{6} d^{16} x^{15} \log {\left (F \right )}^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.77, size = 854, normalized size = 7.56 \begin {gather*} \frac {F^a\,F^{\frac {b}{c^3+3\,c^2\,d\,x+3\,c\,d^2\,x^2+d^3\,x^3}}\,\left (\frac {40\,x^{15}}{b^6\,d\,{\ln \left (F\right )}^6}-\frac {b^5\,{\ln \left (F\right )}^5-5\,b^4\,c^3\,{\ln \left (F\right )}^4+20\,b^3\,c^6\,{\ln \left (F\right )}^3-60\,b^2\,c^9\,{\ln \left (F\right )}^2+120\,b\,c^{12}\,\ln \left (F\right )-120\,c^{15}}{3\,b^6\,d^{16}\,{\ln \left (F\right )}^6}+\frac {600\,c\,x^{14}}{b^6\,d^2\,{\ln \left (F\right )}^6}+\frac {4200\,c^2\,x^{13}}{b^6\,d^3\,{\ln \left (F\right )}^6}+\frac {5\,x^3\,\left (b^4\,{\ln \left (F\right )}^4-80\,b^3\,c^3\,{\ln \left (F\right )}^3+1008\,b^2\,c^6\,{\ln \left (F\right )}^2-5280\,b\,c^9\,\ln \left (F\right )+10920\,c^{12}\right )}{3\,b^6\,d^{13}\,{\ln \left (F\right )}^6}-\frac {20\,x^6\,\left (b^3\,{\ln \left (F\right )}^3-252\,b^2\,c^3\,{\ln \left (F\right )}^2+5544\,b\,c^6\,\ln \left (F\right )-30030\,c^9\right )}{3\,b^6\,d^{10}\,{\ln \left (F\right )}^6}+\frac {20\,x^9\,\left (b^2\,{\ln \left (F\right )}^2-440\,b\,c^3\,\ln \left (F\right )+10010\,c^6\right )}{b^6\,d^7\,{\ln \left (F\right )}^6}-\frac {40\,x^{12}\,\left (b\,\ln \left (F\right )-455\,c^3\right )}{b^6\,d^4\,{\ln \left (F\right )}^6}+\frac {5\,c^2\,x\,\left (b^4\,{\ln \left (F\right )}^4-8\,b^3\,c^3\,{\ln \left (F\right )}^3+36\,b^2\,c^6\,{\ln \left (F\right )}^2-96\,b\,c^9\,\ln \left (F\right )+120\,c^{12}\right )}{b^6\,d^{15}\,{\ln \left (F\right )}^6}+\frac {5\,c\,x^2\,\left (b^4\,{\ln \left (F\right )}^4-20\,b^3\,c^3\,{\ln \left (F\right )}^3+144\,b^2\,c^6\,{\ln \left (F\right )}^2-528\,b\,c^9\,\ln \left (F\right )+840\,c^{12}\right )}{b^6\,d^{14}\,{\ln \left (F\right )}^6}-\frac {40\,c\,x^5\,\left (b^3\,{\ln \left (F\right )}^3-63\,b^2\,c^3\,{\ln \left (F\right )}^2+792\,b\,c^6\,\ln \left (F\right )-3003\,c^9\right )}{b^6\,d^{11}\,{\ln \left (F\right )}^6}+\frac {180\,c\,x^8\,\left (b^2\,{\ln \left (F\right )}^2-110\,b\,c^3\,\ln \left (F\right )+1430\,c^6\right )}{b^6\,d^8\,{\ln \left (F\right )}^6}-\frac {120\,c\,x^{11}\,\left (4\,b\,\ln \left (F\right )-455\,c^3\right )}{b^6\,d^5\,{\ln \left (F\right )}^6}-\frac {20\,c^2\,x^4\,\left (5\,b^3\,{\ln \left (F\right )}^3-126\,b^2\,c^3\,{\ln \left (F\right )}^2+990\,b\,c^6\,\ln \left (F\right )-2730\,c^9\right )}{b^6\,d^{12}\,{\ln \left (F\right )}^6}+\frac {360\,c^2\,x^7\,\left (2\,b^2\,{\ln \left (F\right )}^2-88\,b\,c^3\,\ln \left (F\right )+715\,c^6\right )}{b^6\,d^9\,{\ln \left (F\right )}^6}-\frac {1320\,c^2\,x^{10}\,\left (2\,b\,\ln \left (F\right )-91\,c^3\right )}{b^6\,d^6\,{\ln \left (F\right )}^6}\right )}{x^{15}+\frac {c^{15}}{d^{15}}+\frac {15\,c\,x^{14}}{d}+\frac {15\,c^{14}\,x}{d^{14}}+\frac {105\,c^2\,x^{13}}{d^2}+\frac {455\,c^3\,x^{12}}{d^3}+\frac {1365\,c^4\,x^{11}}{d^4}+\frac {3003\,c^5\,x^{10}}{d^5}+\frac {5005\,c^6\,x^9}{d^6}+\frac {6435\,c^7\,x^8}{d^7}+\frac {6435\,c^8\,x^7}{d^8}+\frac {5005\,c^9\,x^6}{d^9}+\frac {3003\,c^{10}\,x^5}{d^{10}}+\frac {1365\,c^{11}\,x^4}{d^{11}}+\frac {455\,c^{12}\,x^3}{d^{12}}+\frac {105\,c^{13}\,x^2}{d^{13}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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