Optimal. Leaf size=424 \[ \frac {c^4 x}{e^8}-\frac {\left (c d^2-b d e+a e^2\right )^4}{7 e^9 (d+e x)^7}+\frac {2 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^3}{3 e^9 (d+e x)^6}-\frac {2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{5 e^9 (d+e x)^5}+\frac {(2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right )}{e^9 (d+e x)^4}-\frac {70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )}{3 e^9 (d+e x)^3}+\frac {2 c (2 c d-b e) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right )}{e^9 (d+e x)^2}-\frac {2 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^9 (d+e x)}-\frac {4 c^3 (2 c d-b e) \log (d+e x)}{e^9} \]
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Rubi [A]
time = 0.33, antiderivative size = 424, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {712}
\begin {gather*} -\frac {6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{3 e^9 (d+e x)^3}-\frac {2 c^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{e^9 (d+e x)}+\frac {2 c (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)^2}+\frac {(2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{e^9 (d+e x)^4}-\frac {2 \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{5 e^9 (d+e x)^5}+\frac {2 (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{3 e^9 (d+e x)^6}-\frac {\left (a e^2-b d e+c d^2\right )^4}{7 e^9 (d+e x)^7}-\frac {4 c^3 (2 c d-b e) \log (d+e x)}{e^9}+\frac {c^4 x}{e^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 712
Rubi steps
\begin {align*} \int \frac {\left (a+b x+c x^2\right )^4}{(d+e x)^8} \, dx &=\int \left (\frac {c^4}{e^8}+\frac {\left (c d^2-b d e+a e^2\right )^4}{e^8 (d+e x)^8}+\frac {4 (-2 c d+b e) \left (c d^2-b d e+a e^2\right )^3}{e^8 (d+e x)^7}+\frac {2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^8 (d+e x)^6}+\frac {4 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (-7 c^2 d^2+7 b c d e-b^2 e^2-3 a c e^2\right )}{e^8 (d+e x)^5}+\frac {70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )}{e^8 (d+e x)^4}+\frac {4 c (2 c d-b e) \left (-7 c^2 d^2-b^2 e^2+c e (7 b d-3 a e)\right )}{e^8 (d+e x)^3}+\frac {2 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^8 (d+e x)^2}-\frac {4 c^3 (2 c d-b e)}{e^8 (d+e x)}\right ) \, dx\\ &=\frac {c^4 x}{e^8}-\frac {\left (c d^2-b d e+a e^2\right )^4}{7 e^9 (d+e x)^7}+\frac {2 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^3}{3 e^9 (d+e x)^6}-\frac {2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{5 e^9 (d+e x)^5}+\frac {(2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right )}{e^9 (d+e x)^4}-\frac {70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )}{3 e^9 (d+e x)^3}+\frac {2 c (2 c d-b e) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right )}{e^9 (d+e x)^2}-\frac {2 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right )}{e^9 (d+e x)}-\frac {4 c^3 (2 c d-b e) \log (d+e x)}{e^9}\\ \end {align*}
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Mathematica [A]
time = 0.44, size = 748, normalized size = 1.76 \begin {gather*} -\frac {c^4 \left (1443 d^8+9261 d^7 e x+24843 d^6 e^2 x^2+35525 d^5 e^3 x^3+28175 d^4 e^4 x^4+11025 d^3 e^5 x^5+735 d^2 e^6 x^6-735 d e^7 x^7-105 e^8 x^8\right )+e^4 \left (15 a^4 e^4+10 a^3 b e^3 (d+7 e x)+6 a^2 b^2 e^2 \left (d^2+7 d e x+21 e^2 x^2\right )+3 a b^3 e \left (d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right )+b^4 \left (d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right )\right )+c e^3 \left (4 a^3 e^3 \left (d^2+7 d e x+21 e^2 x^2\right )+9 a^2 b e^2 \left (d^3+7 d^2 e x+21 d e^2 x^2+35 e^3 x^3\right )+12 a b^2 e \left (d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right )+10 b^3 \left (d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right )\right )+6 c^2 e^2 \left (a^2 e^2 \left (d^4+7 d^3 e x+21 d^2 e^2 x^2+35 d e^3 x^3+35 e^4 x^4\right )+5 a b e \left (d^5+7 d^4 e x+21 d^3 e^2 x^2+35 d^2 e^3 x^3+35 d e^4 x^4+21 e^5 x^5\right )+15 b^2 \left (d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right )\right )+c^3 e \left (60 a e \left (d^6+7 d^5 e x+21 d^4 e^2 x^2+35 d^3 e^3 x^3+35 d^2 e^4 x^4+21 d e^5 x^5+7 e^6 x^6\right )-b d \left (1089 d^6+7203 d^5 e x+20139 d^4 e^2 x^2+30625 d^3 e^3 x^3+26950 d^2 e^4 x^4+13230 d e^5 x^5+2940 e^6 x^6\right )\right )+420 c^3 (2 c d-b e) (d+e x)^7 \log (d+e x)}{105 e^9 (d+e x)^7} \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. \(905\) vs.
\(2(417)=834\).
time = 0.75, size = 906, normalized size = 2.14 Too large to display
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. 881 vs.
\(2 (423) = 846\).
time = 0.31, size = 881, normalized size = 2.08 \begin {gather*} c^{4} x e^{\left (-8\right )} - 4 \, {\left (2 \, c^{4} d - b c^{3} e\right )} e^{\left (-9\right )} \log \left (x e + d\right ) - \frac {1443 \, c^{4} d^{8} - 1089 \, b c^{3} d^{7} e + 30 \, {\left (3 \, b^{2} c^{2} e^{2} + 2 \, a c^{3} e^{2}\right )} d^{6} + 210 \, {\left (14 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} + 3 \, b^{2} c^{2} e^{8} + 2 \, a c^{3} e^{8}\right )} x^{6} + 10 \, {\left (b^{3} c e^{3} + 3 \, a b c^{2} e^{3}\right )} d^{5} + 210 \, {\left (70 \, c^{4} d^{3} e^{5} - 63 \, b c^{3} d^{2} e^{6} + b^{3} c e^{8} + 3 \, a b c^{2} e^{8} + 3 \, {\left (3 \, b^{2} c^{2} e^{7} + 2 \, a c^{3} e^{7}\right )} d\right )} x^{5} + 10 \, a^{3} b d e^{7} + {\left (b^{4} e^{4} + 12 \, a b^{2} c e^{4} + 6 \, a^{2} c^{2} e^{4}\right )} d^{4} + 35 \, {\left (910 \, c^{4} d^{4} e^{4} - 770 \, b c^{3} d^{3} e^{5} + b^{4} e^{8} + 12 \, a b^{2} c e^{8} + 6 \, a^{2} c^{2} e^{8} + 30 \, {\left (3 \, b^{2} c^{2} e^{6} + 2 \, a c^{3} e^{6}\right )} d^{2} + 10 \, {\left (b^{3} c e^{7} + 3 \, a b c^{2} e^{7}\right )} d\right )} x^{4} + 15 \, a^{4} e^{8} + 3 \, {\left (a b^{3} e^{5} + 3 \, a^{2} b c e^{5}\right )} d^{3} + 35 \, {\left (1078 \, c^{4} d^{5} e^{3} - 875 \, b c^{3} d^{4} e^{4} + 3 \, a b^{3} e^{8} + 9 \, a^{2} b c e^{8} + 30 \, {\left (3 \, b^{2} c^{2} e^{5} + 2 \, a c^{3} e^{5}\right )} d^{3} + 10 \, {\left (b^{3} c e^{6} + 3 \, a b c^{2} e^{6}\right )} d^{2} + {\left (b^{4} e^{7} + 12 \, a b^{2} c e^{7} + 6 \, a^{2} c^{2} e^{7}\right )} d\right )} x^{3} + 2 \, {\left (3 \, a^{2} b^{2} e^{6} + 2 \, a^{3} c e^{6}\right )} d^{2} + 21 \, {\left (1218 \, c^{4} d^{6} e^{2} - 959 \, b c^{3} d^{5} e^{3} + 30 \, {\left (3 \, b^{2} c^{2} e^{4} + 2 \, a c^{3} e^{4}\right )} d^{4} + 6 \, a^{2} b^{2} e^{8} + 4 \, a^{3} c e^{8} + 10 \, {\left (b^{3} c e^{5} + 3 \, a b c^{2} e^{5}\right )} d^{3} + {\left (b^{4} e^{6} + 12 \, a b^{2} c e^{6} + 6 \, a^{2} c^{2} e^{6}\right )} d^{2} + 3 \, {\left (a b^{3} e^{7} + 3 \, a^{2} b c e^{7}\right )} d\right )} x^{2} + 7 \, {\left (1338 \, c^{4} d^{7} e - 1029 \, b c^{3} d^{6} e^{2} + 30 \, {\left (3 \, b^{2} c^{2} e^{3} + 2 \, a c^{3} e^{3}\right )} d^{5} + 10 \, {\left (b^{3} c e^{4} + 3 \, a b c^{2} e^{4}\right )} d^{4} + 10 \, a^{3} b e^{8} + {\left (b^{4} e^{5} + 12 \, a b^{2} c e^{5} + 6 \, a^{2} c^{2} e^{5}\right )} d^{3} + 3 \, {\left (a b^{3} e^{6} + 3 \, a^{2} b c e^{6}\right )} d^{2} + 2 \, {\left (3 \, a^{2} b^{2} e^{7} + 2 \, a^{3} c e^{7}\right )} d\right )} x}{105 \, {\left (x^{7} e^{16} + 7 \, d x^{6} e^{15} + 21 \, d^{2} x^{5} e^{14} + 35 \, d^{3} x^{4} e^{13} + 35 \, d^{4} x^{3} e^{12} + 21 \, d^{5} x^{2} e^{11} + 7 \, d^{6} x e^{10} + d^{7} e^{9}\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. 1031 vs.
\(2 (423) = 846\).
time = 2.14, size = 1031, normalized size = 2.43 \begin {gather*} -\frac {1443 \, c^{4} d^{8} - {\left (105 \, c^{4} x^{8} - 210 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} x^{6} - 210 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} x^{5} - 70 \, a^{3} b x - 35 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} x^{4} - 15 \, a^{4} - 105 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} x^{3} - 42 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} x^{2}\right )} e^{8} - {\left (735 \, c^{4} d x^{7} + 2940 \, b c^{3} d x^{6} - 630 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d x^{5} - 350 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d x^{4} - 10 \, a^{3} b d - 35 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d x^{3} - 63 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d x^{2} - 14 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d x\right )} e^{7} + {\left (735 \, c^{4} d^{2} x^{6} - 13230 \, b c^{3} d^{2} x^{5} + 1050 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{2} x^{4} + 350 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{2} x^{3} + 21 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{2} x^{2} + 21 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{2} x + 2 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d^{2}\right )} e^{6} + {\left (11025 \, c^{4} d^{3} x^{5} - 26950 \, b c^{3} d^{3} x^{4} + 1050 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{3} x^{3} + 210 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{3} x^{2} + 7 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{3} x + 3 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{3}\right )} e^{5} + {\left (28175 \, c^{4} d^{4} x^{4} - 30625 \, b c^{3} d^{4} x^{3} + 630 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{4} x^{2} + 70 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{4} x + {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{4}\right )} e^{4} + {\left (35525 \, c^{4} d^{5} x^{3} - 20139 \, b c^{3} d^{5} x^{2} + 210 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{5} x + 10 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{5}\right )} e^{3} + 3 \, {\left (8281 \, c^{4} d^{6} x^{2} - 2401 \, b c^{3} d^{6} x + 10 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{6}\right )} e^{2} + 9 \, {\left (1029 \, c^{4} d^{7} x - 121 \, b c^{3} d^{7}\right )} e + 420 \, {\left (2 \, c^{4} d^{8} - b c^{3} x^{7} e^{8} + {\left (2 \, c^{4} d x^{7} - 7 \, b c^{3} d x^{6}\right )} e^{7} + 7 \, {\left (2 \, c^{4} d^{2} x^{6} - 3 \, b c^{3} d^{2} x^{5}\right )} e^{6} + 7 \, {\left (6 \, c^{4} d^{3} x^{5} - 5 \, b c^{3} d^{3} x^{4}\right )} e^{5} + 35 \, {\left (2 \, c^{4} d^{4} x^{4} - b c^{3} d^{4} x^{3}\right )} e^{4} + 7 \, {\left (10 \, c^{4} d^{5} x^{3} - 3 \, b c^{3} d^{5} x^{2}\right )} e^{3} + 7 \, {\left (6 \, c^{4} d^{6} x^{2} - b c^{3} d^{6} x\right )} e^{2} + {\left (14 \, c^{4} d^{7} x - b c^{3} d^{7}\right )} e\right )} \log \left (x e + d\right )}{105 \, {\left (x^{7} e^{16} + 7 \, d x^{6} e^{15} + 21 \, d^{2} x^{5} e^{14} + 35 \, d^{3} x^{4} e^{13} + 35 \, d^{4} x^{3} e^{12} + 21 \, d^{5} x^{2} e^{11} + 7 \, d^{6} x e^{10} + d^{7} e^{9}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.14, size = 833, normalized size = 1.96 \begin {gather*} c^{4} x e^{\left (-8\right )} - 4 \, {\left (2 \, c^{4} d - b c^{3} e\right )} e^{\left (-9\right )} \log \left ({\left | x e + d \right |}\right ) - \frac {{\left (1443 \, c^{4} d^{8} - 1089 \, b c^{3} d^{7} e + 90 \, b^{2} c^{2} d^{6} e^{2} + 60 \, a c^{3} d^{6} e^{2} + 10 \, b^{3} c d^{5} e^{3} + 30 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} + 3 \, a b^{3} d^{3} e^{5} + 9 \, a^{2} b c d^{3} e^{5} + 210 \, {\left (14 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} + 3 \, b^{2} c^{2} e^{8} + 2 \, a c^{3} e^{8}\right )} x^{6} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} + 210 \, {\left (70 \, c^{4} d^{3} e^{5} - 63 \, b c^{3} d^{2} e^{6} + 9 \, b^{2} c^{2} d e^{7} + 6 \, a c^{3} d e^{7} + b^{3} c e^{8} + 3 \, a b c^{2} e^{8}\right )} x^{5} + 10 \, a^{3} b d e^{7} + 35 \, {\left (910 \, c^{4} d^{4} e^{4} - 770 \, b c^{3} d^{3} e^{5} + 90 \, b^{2} c^{2} d^{2} e^{6} + 60 \, a c^{3} d^{2} e^{6} + 10 \, b^{3} c d e^{7} + 30 \, a b c^{2} d e^{7} + b^{4} e^{8} + 12 \, a b^{2} c e^{8} + 6 \, a^{2} c^{2} e^{8}\right )} x^{4} + 15 \, a^{4} e^{8} + 35 \, {\left (1078 \, c^{4} d^{5} e^{3} - 875 \, b c^{3} d^{4} e^{4} + 90 \, b^{2} c^{2} d^{3} e^{5} + 60 \, a c^{3} d^{3} e^{5} + 10 \, b^{3} c d^{2} e^{6} + 30 \, a b c^{2} d^{2} e^{6} + b^{4} d e^{7} + 12 \, a b^{2} c d e^{7} + 6 \, a^{2} c^{2} d e^{7} + 3 \, a b^{3} e^{8} + 9 \, a^{2} b c e^{8}\right )} x^{3} + 21 \, {\left (1218 \, c^{4} d^{6} e^{2} - 959 \, b c^{3} d^{5} e^{3} + 90 \, b^{2} c^{2} d^{4} e^{4} + 60 \, a c^{3} d^{4} e^{4} + 10 \, b^{3} c d^{3} e^{5} + 30 \, a b c^{2} d^{3} e^{5} + b^{4} d^{2} e^{6} + 12 \, a b^{2} c d^{2} e^{6} + 6 \, a^{2} c^{2} d^{2} e^{6} + 3 \, a b^{3} d e^{7} + 9 \, a^{2} b c d e^{7} + 6 \, a^{2} b^{2} e^{8} + 4 \, a^{3} c e^{8}\right )} x^{2} + 7 \, {\left (1338 \, c^{4} d^{7} e - 1029 \, b c^{3} d^{6} e^{2} + 90 \, b^{2} c^{2} d^{5} e^{3} + 60 \, a c^{3} d^{5} e^{3} + 10 \, b^{3} c d^{4} e^{4} + 30 \, a b c^{2} d^{4} e^{4} + b^{4} d^{3} e^{5} + 12 \, a b^{2} c d^{3} e^{5} + 6 \, a^{2} c^{2} d^{3} e^{5} + 3 \, a b^{3} d^{2} e^{6} + 9 \, a^{2} b c d^{2} e^{6} + 6 \, a^{2} b^{2} d e^{7} + 4 \, a^{3} c d e^{7} + 10 \, a^{3} b e^{8}\right )} x\right )} e^{\left (-9\right )}}{105 \, {\left (x e + d\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.95, size = 1306, normalized size = 3.08 \begin {gather*} -\frac {\frac {a^4\,e^8}{7}+\frac {481\,c^4\,d^8}{35}+8\,c^4\,d^8\,\ln \left (d+e\,x\right )+\frac {b^4\,d^4\,e^4}{105}+\frac {b^4\,e^8\,x^4}{3}-c^4\,e^8\,x^8+\frac {a\,b^3\,d^3\,e^5}{35}+\frac {4\,a\,c^3\,d^6\,e^2}{7}+\frac {4\,a^3\,c\,d^2\,e^6}{105}+\frac {2\,b^3\,c\,d^5\,e^3}{21}+a\,b^3\,e^8\,x^3+\frac {4\,a^3\,c\,e^8\,x^2}{5}+4\,a\,c^3\,e^8\,x^6+2\,b^3\,c\,e^8\,x^5+\frac {b^4\,d^3\,e^5\,x}{15}+\frac {b^4\,d\,e^7\,x^3}{3}-7\,c^4\,d\,e^7\,x^7+\frac {2\,a^2\,b^2\,d^2\,e^6}{35}+\frac {2\,a^2\,c^2\,d^4\,e^4}{35}+\frac {6\,b^2\,c^2\,d^6\,e^2}{7}+\frac {6\,a^2\,b^2\,e^8\,x^2}{5}+2\,a^2\,c^2\,e^8\,x^4+6\,b^2\,c^2\,e^8\,x^6+\frac {b^4\,d^2\,e^6\,x^2}{5}+\frac {1183\,c^4\,d^6\,e^2\,x^2}{5}+\frac {1015\,c^4\,d^5\,e^3\,x^3}{3}+\frac {805\,c^4\,d^4\,e^4\,x^4}{3}+105\,c^4\,d^3\,e^5\,x^5+7\,c^4\,d^2\,e^6\,x^6+\frac {2\,a^3\,b\,d\,e^7}{21}-\frac {363\,b\,c^3\,d^7\,e}{35}+\frac {2\,a^3\,b\,e^8\,x}{3}+\frac {441\,c^4\,d^7\,e\,x}{5}-4\,b\,c^3\,d^7\,e\,\ln \left (d+e\,x\right )+\frac {4\,a^3\,c\,d\,e^7\,x}{15}+56\,c^4\,d^7\,e\,x\,\ln \left (d+e\,x\right )+\frac {6\,a^2\,c^2\,d^2\,e^6\,x^2}{5}+18\,b^2\,c^2\,d^4\,e^4\,x^2+30\,b^2\,c^2\,d^3\,e^5\,x^3+30\,b^2\,c^2\,d^2\,e^6\,x^4+\frac {2\,a\,b\,c^2\,d^5\,e^3}{7}+\frac {4\,a\,b^2\,c\,d^4\,e^4}{35}+\frac {3\,a^2\,b\,c\,d^3\,e^5}{35}+3\,a^2\,b\,c\,e^8\,x^3+4\,a\,b^2\,c\,e^8\,x^4+6\,a\,b\,c^2\,e^8\,x^5+\frac {a\,b^3\,d^2\,e^6\,x}{5}+\frac {2\,a^2\,b^2\,d\,e^7\,x}{5}+\frac {3\,a\,b^3\,d\,e^7\,x^2}{5}+4\,a\,c^3\,d^5\,e^3\,x+12\,a\,c^3\,d\,e^7\,x^5-\frac {343\,b\,c^3\,d^6\,e^2\,x}{5}+\frac {2\,b^3\,c\,d^4\,e^4\,x}{3}+\frac {10\,b^3\,c\,d\,e^7\,x^4}{3}-28\,b\,c^3\,d\,e^7\,x^6-4\,b\,c^3\,e^8\,x^7\,\ln \left (d+e\,x\right )+8\,c^4\,d\,e^7\,x^7\,\ln \left (d+e\,x\right )+\frac {2\,a^2\,c^2\,d^3\,e^5\,x}{5}+12\,a\,c^3\,d^4\,e^4\,x^2+20\,a\,c^3\,d^3\,e^5\,x^3+2\,a^2\,c^2\,d\,e^7\,x^3+20\,a\,c^3\,d^2\,e^6\,x^4+6\,b^2\,c^2\,d^5\,e^3\,x-\frac {959\,b\,c^3\,d^5\,e^3\,x^2}{5}+2\,b^3\,c\,d^3\,e^5\,x^2-\frac {875\,b\,c^3\,d^4\,e^4\,x^3}{3}+\frac {10\,b^3\,c\,d^2\,e^6\,x^3}{3}-\frac {770\,b\,c^3\,d^3\,e^5\,x^4}{3}-126\,b\,c^3\,d^2\,e^6\,x^5+18\,b^2\,c^2\,d\,e^7\,x^5+168\,c^4\,d^6\,e^2\,x^2\,\ln \left (d+e\,x\right )+280\,c^4\,d^5\,e^3\,x^3\,\ln \left (d+e\,x\right )+280\,c^4\,d^4\,e^4\,x^4\,\ln \left (d+e\,x\right )+168\,c^4\,d^3\,e^5\,x^5\,\ln \left (d+e\,x\right )+56\,c^4\,d^2\,e^6\,x^6\,\ln \left (d+e\,x\right )+6\,a\,b\,c^2\,d^3\,e^5\,x^2+\frac {12\,a\,b^2\,c\,d^2\,e^6\,x^2}{5}+10\,a\,b\,c^2\,d^2\,e^6\,x^3-84\,b\,c^3\,d^5\,e^3\,x^2\,\ln \left (d+e\,x\right )-140\,b\,c^3\,d^4\,e^4\,x^3\,\ln \left (d+e\,x\right )-140\,b\,c^3\,d^3\,e^5\,x^4\,\ln \left (d+e\,x\right )-84\,b\,c^3\,d^2\,e^6\,x^5\,\ln \left (d+e\,x\right )+2\,a\,b\,c^2\,d^4\,e^4\,x+\frac {4\,a\,b^2\,c\,d^3\,e^5\,x}{5}+\frac {3\,a^2\,b\,c\,d^2\,e^6\,x}{5}+\frac {9\,a^2\,b\,c\,d\,e^7\,x^2}{5}+4\,a\,b^2\,c\,d\,e^7\,x^3+10\,a\,b\,c^2\,d\,e^7\,x^4-28\,b\,c^3\,d^6\,e^2\,x\,\ln \left (d+e\,x\right )-28\,b\,c^3\,d\,e^7\,x^6\,\ln \left (d+e\,x\right )}{e^9\,{\left (d+e\,x\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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