Integrand size = 24, antiderivative size = 101 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=-\frac {\left (b^2-4 a c\right )^3 d^5 (b+2 c x)^6}{768 c^4}+\frac {3 \left (b^2-4 a c\right )^2 d^5 (b+2 c x)^8}{1024 c^4}-\frac {3 \left (b^2-4 a c\right ) d^5 (b+2 c x)^{10}}{1280 c^4}+\frac {d^5 (b+2 c x)^{12}}{1536 c^4} \]
[Out]
Time = 0.17 (sec) , antiderivative size = 101, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {697} \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=-\frac {3 d^5 \left (b^2-4 a c\right ) (b+2 c x)^{10}}{1280 c^4}+\frac {3 d^5 \left (b^2-4 a c\right )^2 (b+2 c x)^8}{1024 c^4}-\frac {d^5 \left (b^2-4 a c\right )^3 (b+2 c x)^6}{768 c^4}+\frac {d^5 (b+2 c x)^{12}}{1536 c^4} \]
[In]
[Out]
Rule 697
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {\left (-b^2+4 a c\right )^3 (b d+2 c d x)^5}{64 c^3}+\frac {3 \left (-b^2+4 a c\right )^2 (b d+2 c d x)^7}{64 c^3 d^2}+\frac {3 \left (-b^2+4 a c\right ) (b d+2 c d x)^9}{64 c^3 d^4}+\frac {(b d+2 c d x)^{11}}{64 c^3 d^6}\right ) \, dx \\ & = -\frac {\left (b^2-4 a c\right )^3 d^5 (b+2 c x)^6}{768 c^4}+\frac {3 \left (b^2-4 a c\right )^2 d^5 (b+2 c x)^8}{1024 c^4}-\frac {3 \left (b^2-4 a c\right ) d^5 (b+2 c x)^{10}}{1280 c^4}+\frac {d^5 (b+2 c x)^{12}}{1536 c^4} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(224\) vs. \(2(101)=202\).
Time = 0.09 (sec) , antiderivative size = 224, normalized size of antiderivative = 2.22 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=\frac {1}{60} d^5 x (b+c x) \left (20 a^3 \left (3 b^4+12 b^3 c x+28 b^2 c^2 x^2+32 b c^3 x^3+16 c^4 x^4\right )+12 a x^2 (b+c x)^2 \left (5 b^4+30 b^3 c x+78 b^2 c^2 x^2+96 b c^3 x^3+48 c^4 x^4\right )+x^3 (b+c x)^3 \left (15 b^4+96 b^3 c x+256 b^2 c^2 x^2+320 b c^3 x^3+160 c^4 x^4\right )+30 a^2 x \left (3 b^5+19 b^4 c x+56 b^3 c^2 x^2+88 b^2 c^3 x^3+72 b c^4 x^4+24 c^5 x^5\right )\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(337\) vs. \(2(93)=186\).
Time = 2.30 (sec) , antiderivative size = 338, normalized size of antiderivative = 3.35
method | result | size |
gosper | \(\frac {x \left (160 c^{8} x^{11}+960 b \,c^{7} x^{10}+576 x^{9} c^{7} a +2496 x^{9} b^{2} c^{6}+2880 x^{8} a b \,c^{6}+3680 x^{8} b^{3} c^{5}+720 x^{7} a^{2} c^{6}+6120 x^{7} a \,b^{2} c^{5}+3375 x^{7} b^{4} c^{4}+2880 a^{2} b \,c^{5} x^{6}+7200 a \,b^{3} c^{4} x^{6}+1980 b^{5} c^{3} x^{6}+320 x^{5} a^{3} c^{5}+4800 x^{5} a^{2} b^{2} c^{4}+5100 x^{5} a \,b^{4} c^{3}+730 x^{5} c^{2} b^{6}+960 x^{4} a^{3} b \,c^{4}+4320 x^{4} a^{2} b^{3} c^{3}+2196 x^{4} a \,b^{5} c^{2}+156 x^{4} b^{7} c +1200 x^{3} a^{3} b^{2} c^{3}+2250 x^{3} a^{2} b^{4} c^{2}+540 x^{3} a \,b^{6} c +15 b^{8} x^{3}+800 x^{2} a^{3} c^{2} b^{3}+660 x^{2} a^{2} b^{5} c +60 x^{2} a \,b^{7}+300 x \,a^{3} b^{4} c +90 a^{2} b^{6} x +60 a^{3} b^{5}\right ) d^{5}}{60}\) | \(338\) |
norman | \(\left (\frac {48}{5} a \,c^{7} d^{5}+\frac {208}{5} b^{2} d^{5} c^{6}\right ) x^{10}+\left (48 a b \,c^{6} d^{5}+\frac {184}{3} b^{3} d^{5} c^{5}\right ) x^{9}+\left (5 b^{4} d^{5} c \,a^{3}+\frac {3}{2} b^{6} d^{5} a^{2}\right ) x^{2}+\left (12 a^{2} c^{6} d^{5}+102 a \,b^{2} c^{5} d^{5}+\frac {225}{4} b^{4} c^{4} d^{5}\right ) x^{8}+\left (\frac {40}{3} b^{3} d^{5} c^{2} a^{3}+11 b^{5} d^{5} c \,a^{2}+a \,b^{7} d^{5}\right ) x^{3}+\left (\frac {16}{3} c^{5} d^{5} a^{3}+80 b^{2} d^{5} c^{4} a^{2}+85 a \,b^{4} c^{3} d^{5}+\frac {73}{6} b^{6} d^{5} c^{2}\right ) x^{6}+\left (16 b \,d^{5} c^{4} a^{3}+72 b^{3} d^{5} c^{3} a^{2}+\frac {183}{5} a \,b^{5} c^{2} d^{5}+\frac {13}{5} b^{7} c \,d^{5}\right ) x^{5}+\left (20 b^{2} d^{5} c^{3} a^{3}+\frac {75}{2} b^{4} d^{5} c^{2} a^{2}+9 a \,b^{6} c \,d^{5}+\frac {1}{4} b^{8} d^{5}\right ) x^{4}+\left (48 c^{5} d^{5} a^{2} b +120 a \,b^{3} c^{4} d^{5}+33 b^{5} d^{5} c^{3}\right ) x^{7}+b^{5} d^{5} a^{3} x +\frac {8 c^{8} d^{5} x^{12}}{3}+16 b \,d^{5} c^{7} x^{11}\) | \(389\) |
risch | \(\frac {8}{3} c^{8} d^{5} x^{12}+16 b \,d^{5} c^{7} x^{11}+\frac {183}{5} d^{5} x^{5} a \,b^{5} c^{2}+\frac {1}{4} d^{5} b^{8} x^{4}+\frac {75}{2} d^{5} x^{4} a^{2} b^{4} c^{2}+9 d^{5} x^{4} a \,b^{6} c +\frac {40}{3} d^{5} x^{3} a^{3} c^{2} b^{3}+11 d^{5} x^{3} a^{2} b^{5} c +5 d^{5} x^{2} a^{3} b^{4} c +48 d^{5} a^{2} b \,c^{5} x^{7}+120 d^{5} a \,b^{3} c^{4} x^{7}+48 d^{5} x^{9} a b \,c^{6}+102 d^{5} x^{8} a \,b^{2} c^{5}+80 d^{5} x^{6} b^{2} c^{4} a^{2}+85 d^{5} x^{6} a \,b^{4} c^{3}+16 d^{5} x^{5} a^{3} b \,c^{4}+\frac {48}{5} d^{5} x^{10} c^{7} a +\frac {208}{5} d^{5} x^{10} b^{2} c^{6}+\frac {184}{3} d^{5} x^{9} b^{3} c^{5}+12 d^{5} x^{8} a^{2} c^{6}+\frac {225}{4} d^{5} x^{8} b^{4} c^{4}+33 d^{5} b^{5} c^{3} x^{7}+\frac {3}{2} d^{5} a^{2} b^{6} x^{2}+d^{5} a \,b^{7} x^{3}+\frac {13}{5} d^{5} x^{5} b^{7} c +\frac {16}{3} d^{5} x^{6} a^{3} c^{5}+\frac {73}{6} d^{5} x^{6} c^{2} b^{6}+b^{5} d^{5} a^{3} x +20 d^{5} x^{4} a^{3} b^{2} c^{3}+72 d^{5} x^{5} a^{2} b^{3} c^{3}\) | \(425\) |
parallelrisch | \(\frac {8}{3} c^{8} d^{5} x^{12}+16 b \,d^{5} c^{7} x^{11}+\frac {183}{5} d^{5} x^{5} a \,b^{5} c^{2}+\frac {1}{4} d^{5} b^{8} x^{4}+\frac {75}{2} d^{5} x^{4} a^{2} b^{4} c^{2}+9 d^{5} x^{4} a \,b^{6} c +\frac {40}{3} d^{5} x^{3} a^{3} c^{2} b^{3}+11 d^{5} x^{3} a^{2} b^{5} c +5 d^{5} x^{2} a^{3} b^{4} c +48 d^{5} a^{2} b \,c^{5} x^{7}+120 d^{5} a \,b^{3} c^{4} x^{7}+48 d^{5} x^{9} a b \,c^{6}+102 d^{5} x^{8} a \,b^{2} c^{5}+80 d^{5} x^{6} b^{2} c^{4} a^{2}+85 d^{5} x^{6} a \,b^{4} c^{3}+16 d^{5} x^{5} a^{3} b \,c^{4}+\frac {48}{5} d^{5} x^{10} c^{7} a +\frac {208}{5} d^{5} x^{10} b^{2} c^{6}+\frac {184}{3} d^{5} x^{9} b^{3} c^{5}+12 d^{5} x^{8} a^{2} c^{6}+\frac {225}{4} d^{5} x^{8} b^{4} c^{4}+33 d^{5} b^{5} c^{3} x^{7}+\frac {3}{2} d^{5} a^{2} b^{6} x^{2}+d^{5} a \,b^{7} x^{3}+\frac {13}{5} d^{5} x^{5} b^{7} c +\frac {16}{3} d^{5} x^{6} a^{3} c^{5}+\frac {73}{6} d^{5} x^{6} c^{2} b^{6}+b^{5} d^{5} a^{3} x +20 d^{5} x^{4} a^{3} b^{2} c^{3}+72 d^{5} x^{5} a^{2} b^{3} c^{3}\) | \(425\) |
default | \(\frac {8 c^{8} d^{5} x^{12}}{3}+16 b \,d^{5} c^{7} x^{11}+\frac {\left (320 b^{2} d^{5} c^{6}+32 c^{5} d^{5} \left (c^{2} a +2 b^{2} c +c \left (2 a c +b^{2}\right )\right )\right ) x^{10}}{10}+\frac {\left (280 b^{3} d^{5} c^{5}+80 b \,d^{5} c^{4} \left (c^{2} a +2 b^{2} c +c \left (2 a c +b^{2}\right )\right )+32 c^{5} d^{5} \left (4 a b c +b \left (2 a c +b^{2}\right )\right )\right ) x^{9}}{9}+\frac {\left (130 b^{4} c^{4} d^{5}+80 b^{2} d^{5} c^{3} \left (c^{2} a +2 b^{2} c +c \left (2 a c +b^{2}\right )\right )+80 b \,d^{5} c^{4} \left (4 a b c +b \left (2 a c +b^{2}\right )\right )+32 c^{5} d^{5} \left (a \left (2 a c +b^{2}\right )+2 a \,b^{2}+a^{2} c \right )\right ) x^{8}}{8}+\frac {\left (31 b^{5} d^{5} c^{3}+40 b^{3} d^{5} c^{2} \left (c^{2} a +2 b^{2} c +c \left (2 a c +b^{2}\right )\right )+80 b^{2} d^{5} c^{3} \left (4 a b c +b \left (2 a c +b^{2}\right )\right )+80 b \,d^{5} c^{4} \left (a \left (2 a c +b^{2}\right )+2 a \,b^{2}+a^{2} c \right )+96 c^{5} d^{5} a^{2} b \right ) x^{7}}{7}+\frac {\left (3 b^{6} d^{5} c^{2}+10 b^{4} d^{5} c \left (c^{2} a +2 b^{2} c +c \left (2 a c +b^{2}\right )\right )+40 b^{3} d^{5} c^{2} \left (4 a b c +b \left (2 a c +b^{2}\right )\right )+80 b^{2} d^{5} c^{3} \left (a \left (2 a c +b^{2}\right )+2 a \,b^{2}+a^{2} c \right )+240 b^{2} d^{5} c^{4} a^{2}+32 c^{5} d^{5} a^{3}\right ) x^{6}}{6}+\frac {\left (b^{5} d^{5} \left (c^{2} a +2 b^{2} c +c \left (2 a c +b^{2}\right )\right )+10 b^{4} d^{5} c \left (4 a b c +b \left (2 a c +b^{2}\right )\right )+40 b^{3} d^{5} c^{2} \left (a \left (2 a c +b^{2}\right )+2 a \,b^{2}+a^{2} c \right )+240 b^{3} d^{5} c^{3} a^{2}+80 b \,d^{5} c^{4} a^{3}\right ) x^{5}}{5}+\frac {\left (b^{5} d^{5} \left (4 a b c +b \left (2 a c +b^{2}\right )\right )+10 b^{4} d^{5} c \left (a \left (2 a c +b^{2}\right )+2 a \,b^{2}+a^{2} c \right )+120 b^{4} d^{5} c^{2} a^{2}+80 b^{2} d^{5} c^{3} a^{3}\right ) x^{4}}{4}+\frac {\left (b^{5} d^{5} \left (a \left (2 a c +b^{2}\right )+2 a \,b^{2}+a^{2} c \right )+30 b^{5} d^{5} c \,a^{2}+40 b^{3} d^{5} c^{2} a^{3}\right ) x^{3}}{3}+\frac {\left (10 b^{4} d^{5} c \,a^{3}+3 b^{6} d^{5} a^{2}\right ) x^{2}}{2}+b^{5} d^{5} a^{3} x\) | \(810\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 342 vs. \(2 (93) = 186\).
Time = 0.26 (sec) , antiderivative size = 342, normalized size of antiderivative = 3.39 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=\frac {8}{3} \, c^{8} d^{5} x^{12} + 16 \, b c^{7} d^{5} x^{11} + \frac {16}{5} \, {\left (13 \, b^{2} c^{6} + 3 \, a c^{7}\right )} d^{5} x^{10} + \frac {8}{3} \, {\left (23 \, b^{3} c^{5} + 18 \, a b c^{6}\right )} d^{5} x^{9} + a^{3} b^{5} d^{5} x + \frac {3}{4} \, {\left (75 \, b^{4} c^{4} + 136 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right )} d^{5} x^{8} + 3 \, {\left (11 \, b^{5} c^{3} + 40 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right )} d^{5} x^{7} + \frac {1}{6} \, {\left (73 \, b^{6} c^{2} + 510 \, a b^{4} c^{3} + 480 \, a^{2} b^{2} c^{4} + 32 \, a^{3} c^{5}\right )} d^{5} x^{6} + \frac {1}{5} \, {\left (13 \, b^{7} c + 183 \, a b^{5} c^{2} + 360 \, a^{2} b^{3} c^{3} + 80 \, a^{3} b c^{4}\right )} d^{5} x^{5} + \frac {1}{4} \, {\left (b^{8} + 36 \, a b^{6} c + 150 \, a^{2} b^{4} c^{2} + 80 \, a^{3} b^{2} c^{3}\right )} d^{5} x^{4} + \frac {1}{3} \, {\left (3 \, a b^{7} + 33 \, a^{2} b^{5} c + 40 \, a^{3} b^{3} c^{2}\right )} d^{5} x^{3} + \frac {1}{2} \, {\left (3 \, a^{2} b^{6} + 10 \, a^{3} b^{4} c\right )} d^{5} x^{2} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 428 vs. \(2 (100) = 200\).
Time = 0.05 (sec) , antiderivative size = 428, normalized size of antiderivative = 4.24 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=a^{3} b^{5} d^{5} x + 16 b c^{7} d^{5} x^{11} + \frac {8 c^{8} d^{5} x^{12}}{3} + x^{10} \cdot \left (\frac {48 a c^{7} d^{5}}{5} + \frac {208 b^{2} c^{6} d^{5}}{5}\right ) + x^{9} \cdot \left (48 a b c^{6} d^{5} + \frac {184 b^{3} c^{5} d^{5}}{3}\right ) + x^{8} \cdot \left (12 a^{2} c^{6} d^{5} + 102 a b^{2} c^{5} d^{5} + \frac {225 b^{4} c^{4} d^{5}}{4}\right ) + x^{7} \cdot \left (48 a^{2} b c^{5} d^{5} + 120 a b^{3} c^{4} d^{5} + 33 b^{5} c^{3} d^{5}\right ) + x^{6} \cdot \left (\frac {16 a^{3} c^{5} d^{5}}{3} + 80 a^{2} b^{2} c^{4} d^{5} + 85 a b^{4} c^{3} d^{5} + \frac {73 b^{6} c^{2} d^{5}}{6}\right ) + x^{5} \cdot \left (16 a^{3} b c^{4} d^{5} + 72 a^{2} b^{3} c^{3} d^{5} + \frac {183 a b^{5} c^{2} d^{5}}{5} + \frac {13 b^{7} c d^{5}}{5}\right ) + x^{4} \cdot \left (20 a^{3} b^{2} c^{3} d^{5} + \frac {75 a^{2} b^{4} c^{2} d^{5}}{2} + 9 a b^{6} c d^{5} + \frac {b^{8} d^{5}}{4}\right ) + x^{3} \cdot \left (\frac {40 a^{3} b^{3} c^{2} d^{5}}{3} + 11 a^{2} b^{5} c d^{5} + a b^{7} d^{5}\right ) + x^{2} \cdot \left (5 a^{3} b^{4} c d^{5} + \frac {3 a^{2} b^{6} d^{5}}{2}\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 342 vs. \(2 (93) = 186\).
Time = 0.19 (sec) , antiderivative size = 342, normalized size of antiderivative = 3.39 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=\frac {8}{3} \, c^{8} d^{5} x^{12} + 16 \, b c^{7} d^{5} x^{11} + \frac {16}{5} \, {\left (13 \, b^{2} c^{6} + 3 \, a c^{7}\right )} d^{5} x^{10} + \frac {8}{3} \, {\left (23 \, b^{3} c^{5} + 18 \, a b c^{6}\right )} d^{5} x^{9} + a^{3} b^{5} d^{5} x + \frac {3}{4} \, {\left (75 \, b^{4} c^{4} + 136 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right )} d^{5} x^{8} + 3 \, {\left (11 \, b^{5} c^{3} + 40 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right )} d^{5} x^{7} + \frac {1}{6} \, {\left (73 \, b^{6} c^{2} + 510 \, a b^{4} c^{3} + 480 \, a^{2} b^{2} c^{4} + 32 \, a^{3} c^{5}\right )} d^{5} x^{6} + \frac {1}{5} \, {\left (13 \, b^{7} c + 183 \, a b^{5} c^{2} + 360 \, a^{2} b^{3} c^{3} + 80 \, a^{3} b c^{4}\right )} d^{5} x^{5} + \frac {1}{4} \, {\left (b^{8} + 36 \, a b^{6} c + 150 \, a^{2} b^{4} c^{2} + 80 \, a^{3} b^{2} c^{3}\right )} d^{5} x^{4} + \frac {1}{3} \, {\left (3 \, a b^{7} + 33 \, a^{2} b^{5} c + 40 \, a^{3} b^{3} c^{2}\right )} d^{5} x^{3} + \frac {1}{2} \, {\left (3 \, a^{2} b^{6} + 10 \, a^{3} b^{4} c\right )} d^{5} x^{2} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 424 vs. \(2 (93) = 186\).
Time = 0.28 (sec) , antiderivative size = 424, normalized size of antiderivative = 4.20 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=\frac {8}{3} \, c^{8} d^{5} x^{12} + 16 \, b c^{7} d^{5} x^{11} + \frac {208}{5} \, b^{2} c^{6} d^{5} x^{10} + \frac {48}{5} \, a c^{7} d^{5} x^{10} + \frac {184}{3} \, b^{3} c^{5} d^{5} x^{9} + 48 \, a b c^{6} d^{5} x^{9} + \frac {225}{4} \, b^{4} c^{4} d^{5} x^{8} + 102 \, a b^{2} c^{5} d^{5} x^{8} + 12 \, a^{2} c^{6} d^{5} x^{8} + 33 \, b^{5} c^{3} d^{5} x^{7} + 120 \, a b^{3} c^{4} d^{5} x^{7} + 48 \, a^{2} b c^{5} d^{5} x^{7} + \frac {73}{6} \, b^{6} c^{2} d^{5} x^{6} + 85 \, a b^{4} c^{3} d^{5} x^{6} + 80 \, a^{2} b^{2} c^{4} d^{5} x^{6} + \frac {16}{3} \, a^{3} c^{5} d^{5} x^{6} + \frac {13}{5} \, b^{7} c d^{5} x^{5} + \frac {183}{5} \, a b^{5} c^{2} d^{5} x^{5} + 72 \, a^{2} b^{3} c^{3} d^{5} x^{5} + 16 \, a^{3} b c^{4} d^{5} x^{5} + \frac {1}{4} \, b^{8} d^{5} x^{4} + 9 \, a b^{6} c d^{5} x^{4} + \frac {75}{2} \, a^{2} b^{4} c^{2} d^{5} x^{4} + 20 \, a^{3} b^{2} c^{3} d^{5} x^{4} + a b^{7} d^{5} x^{3} + 11 \, a^{2} b^{5} c d^{5} x^{3} + \frac {40}{3} \, a^{3} b^{3} c^{2} d^{5} x^{3} + \frac {3}{2} \, a^{2} b^{6} d^{5} x^{2} + 5 \, a^{3} b^{4} c d^{5} x^{2} + a^{3} b^{5} d^{5} x \]
[In]
[Out]
Time = 0.18 (sec) , antiderivative size = 326, normalized size of antiderivative = 3.23 \[ \int (b d+2 c d x)^5 \left (a+b x+c x^2\right )^3 \, dx=\frac {8\,c^8\,d^5\,x^{12}}{3}+\frac {3\,c^4\,d^5\,x^8\,\left (16\,a^2\,c^2+136\,a\,b^2\,c+75\,b^4\right )}{4}+a^3\,b^5\,d^5\,x+16\,b\,c^7\,d^5\,x^{11}+\frac {b^2\,d^5\,x^4\,\left (80\,a^3\,c^3+150\,a^2\,b^2\,c^2+36\,a\,b^4\,c+b^6\right )}{4}+\frac {16\,c^6\,d^5\,x^{10}\,\left (13\,b^2+3\,a\,c\right )}{5}+\frac {c^2\,d^5\,x^6\,\left (32\,a^3\,c^3+480\,a^2\,b^2\,c^2+510\,a\,b^4\,c+73\,b^6\right )}{6}+\frac {a^2\,b^4\,d^5\,x^2\,\left (3\,b^2+10\,a\,c\right )}{2}+\frac {a\,b^3\,d^5\,x^3\,\left (40\,a^2\,c^2+33\,a\,b^2\,c+3\,b^4\right )}{3}+3\,b\,c^3\,d^5\,x^7\,\left (16\,a^2\,c^2+40\,a\,b^2\,c+11\,b^4\right )+\frac {b\,c\,d^5\,x^5\,\left (80\,a^3\,c^3+360\,a^2\,b^2\,c^2+183\,a\,b^4\,c+13\,b^6\right )}{5}+\frac {8\,b\,c^5\,d^5\,x^9\,\left (23\,b^2+18\,a\,c\right )}{3} \]
[In]
[Out]