Optimal. Leaf size=219 \[ \frac {(b d-a e)^4 (a+b x)^6 \sqrt {a^2+2 a b x+b^2 x^2}}{7 b^5}+\frac {e (b d-a e)^3 (a+b x)^7 \sqrt {a^2+2 a b x+b^2 x^2}}{2 b^5}+\frac {2 e^2 (b d-a e)^2 (a+b x)^8 \sqrt {a^2+2 a b x+b^2 x^2}}{3 b^5}+\frac {2 e^3 (b d-a e) (a+b x)^9 \sqrt {a^2+2 a b x+b^2 x^2}}{5 b^5}+\frac {e^4 (a+b x)^{10} \sqrt {a^2+2 a b x+b^2 x^2}}{11 b^5} \]
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Rubi [A]
time = 0.21, antiderivative size = 219, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {784, 21, 45}
\begin {gather*} \frac {2 e^3 \sqrt {a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)}{5 b^5}+\frac {2 e^2 \sqrt {a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2}{3 b^5}+\frac {e \sqrt {a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3}{2 b^5}+\frac {\sqrt {a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4}{7 b^5}+\frac {e^4 \sqrt {a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 45
Rule 784
Rubi steps
\begin {align*} \int (a+b x) (d+e x)^4 \left (a^2+2 a b x+b^2 x^2\right )^{5/2} \, dx &=\frac {\sqrt {a^2+2 a b x+b^2 x^2} \int (a+b x) \left (a b+b^2 x\right )^5 (d+e x)^4 \, dx}{b^4 \left (a b+b^2 x\right )}\\ &=\frac {\left (b \sqrt {a^2+2 a b x+b^2 x^2}\right ) \int (a+b x)^6 (d+e x)^4 \, dx}{a b+b^2 x}\\ &=\frac {\left (b \sqrt {a^2+2 a b x+b^2 x^2}\right ) \int \left (\frac {(b d-a e)^4 (a+b x)^6}{b^4}+\frac {4 e (b d-a e)^3 (a+b x)^7}{b^4}+\frac {6 e^2 (b d-a e)^2 (a+b x)^8}{b^4}+\frac {4 e^3 (b d-a e) (a+b x)^9}{b^4}+\frac {e^4 (a+b x)^{10}}{b^4}\right ) \, dx}{a b+b^2 x}\\ &=\frac {(b d-a e)^4 (a+b x)^6 \sqrt {a^2+2 a b x+b^2 x^2}}{7 b^5}+\frac {e (b d-a e)^3 (a+b x)^7 \sqrt {a^2+2 a b x+b^2 x^2}}{2 b^5}+\frac {2 e^2 (b d-a e)^2 (a+b x)^8 \sqrt {a^2+2 a b x+b^2 x^2}}{3 b^5}+\frac {2 e^3 (b d-a e) (a+b x)^9 \sqrt {a^2+2 a b x+b^2 x^2}}{5 b^5}+\frac {e^4 (a+b x)^{10} \sqrt {a^2+2 a b x+b^2 x^2}}{11 b^5}\\ \end {align*}
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Mathematica [A]
time = 0.08, size = 371, normalized size = 1.69 \begin {gather*} \frac {x \sqrt {(a+b x)^2} \left (462 a^6 \left (5 d^4+10 d^3 e x+10 d^2 e^2 x^2+5 d e^3 x^3+e^4 x^4\right )+462 a^5 b x \left (15 d^4+40 d^3 e x+45 d^2 e^2 x^2+24 d e^3 x^3+5 e^4 x^4\right )+330 a^4 b^2 x^2 \left (35 d^4+105 d^3 e x+126 d^2 e^2 x^2+70 d e^3 x^3+15 e^4 x^4\right )+165 a^3 b^3 x^3 \left (70 d^4+224 d^3 e x+280 d^2 e^2 x^2+160 d e^3 x^3+35 e^4 x^4\right )+55 a^2 b^4 x^4 \left (126 d^4+420 d^3 e x+540 d^2 e^2 x^2+315 d e^3 x^3+70 e^4 x^4\right )+11 a b^5 x^5 \left (210 d^4+720 d^3 e x+945 d^2 e^2 x^2+560 d e^3 x^3+126 e^4 x^4\right )+b^6 x^6 \left (330 d^4+1155 d^3 e x+1540 d^2 e^2 x^2+924 d e^3 x^3+210 e^4 x^4\right )\right )}{2310 (a+b x)} \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. \(488\) vs.
\(2(154)=308\).
time = 0.07, size = 489, normalized size = 2.23
method | result | size |
gosper | \(\frac {x \left (210 e^{4} b^{6} x^{10}+1386 x^{9} e^{4} a \,b^{5}+924 x^{9} d \,e^{3} b^{6}+3850 x^{8} e^{4} a^{2} b^{4}+6160 x^{8} d \,e^{3} a \,b^{5}+1540 x^{8} d^{2} e^{2} b^{6}+5775 x^{7} e^{4} a^{3} b^{3}+17325 x^{7} d \,e^{3} a^{2} b^{4}+10395 x^{7} d^{2} e^{2} a \,b^{5}+1155 x^{7} d^{3} e \,b^{6}+4950 x^{6} e^{4} a^{4} b^{2}+26400 x^{6} d \,e^{3} a^{3} b^{3}+29700 x^{6} d^{2} e^{2} a^{2} b^{4}+7920 x^{6} d^{3} e a \,b^{5}+330 x^{6} d^{4} b^{6}+2310 a^{5} b \,e^{4} x^{5}+23100 a^{4} b^{2} d \,e^{3} x^{5}+46200 a^{3} b^{3} d^{2} e^{2} x^{5}+23100 a^{2} b^{4} d^{3} e \,x^{5}+2310 a \,b^{5} d^{4} x^{5}+462 x^{4} e^{4} a^{6}+11088 x^{4} d \,e^{3} a^{5} b +41580 x^{4} d^{2} e^{2} a^{4} b^{2}+36960 x^{4} d^{3} e \,a^{3} b^{3}+6930 x^{4} d^{4} a^{2} b^{4}+2310 a^{6} d \,e^{3} x^{3}+20790 a^{5} b \,d^{2} e^{2} x^{3}+34650 a^{4} b^{2} d^{3} e \,x^{3}+11550 a^{3} b^{3} d^{4} x^{3}+4620 a^{6} d^{2} e^{2} x^{2}+18480 a^{5} b \,d^{3} e \,x^{2}+11550 a^{4} b^{2} d^{4} x^{2}+4620 a^{6} d^{3} e x +6930 a^{5} b \,d^{4} x +2310 d^{4} a^{6}\right ) \left (\left (b x +a \right )^{2}\right )^{\frac {5}{2}}}{2310 \left (b x +a \right )^{5}}\) | \(489\) |
default | \(\frac {x \left (210 e^{4} b^{6} x^{10}+1386 x^{9} e^{4} a \,b^{5}+924 x^{9} d \,e^{3} b^{6}+3850 x^{8} e^{4} a^{2} b^{4}+6160 x^{8} d \,e^{3} a \,b^{5}+1540 x^{8} d^{2} e^{2} b^{6}+5775 x^{7} e^{4} a^{3} b^{3}+17325 x^{7} d \,e^{3} a^{2} b^{4}+10395 x^{7} d^{2} e^{2} a \,b^{5}+1155 x^{7} d^{3} e \,b^{6}+4950 x^{6} e^{4} a^{4} b^{2}+26400 x^{6} d \,e^{3} a^{3} b^{3}+29700 x^{6} d^{2} e^{2} a^{2} b^{4}+7920 x^{6} d^{3} e a \,b^{5}+330 x^{6} d^{4} b^{6}+2310 a^{5} b \,e^{4} x^{5}+23100 a^{4} b^{2} d \,e^{3} x^{5}+46200 a^{3} b^{3} d^{2} e^{2} x^{5}+23100 a^{2} b^{4} d^{3} e \,x^{5}+2310 a \,b^{5} d^{4} x^{5}+462 x^{4} e^{4} a^{6}+11088 x^{4} d \,e^{3} a^{5} b +41580 x^{4} d^{2} e^{2} a^{4} b^{2}+36960 x^{4} d^{3} e \,a^{3} b^{3}+6930 x^{4} d^{4} a^{2} b^{4}+2310 a^{6} d \,e^{3} x^{3}+20790 a^{5} b \,d^{2} e^{2} x^{3}+34650 a^{4} b^{2} d^{3} e \,x^{3}+11550 a^{3} b^{3} d^{4} x^{3}+4620 a^{6} d^{2} e^{2} x^{2}+18480 a^{5} b \,d^{3} e \,x^{2}+11550 a^{4} b^{2} d^{4} x^{2}+4620 a^{6} d^{3} e x +6930 a^{5} b \,d^{4} x +2310 d^{4} a^{6}\right ) \left (\left (b x +a \right )^{2}\right )^{\frac {5}{2}}}{2310 \left (b x +a \right )^{5}}\) | \(489\) |
risch | \(\frac {\sqrt {\left (b x +a \right )^{2}}\, e^{4} b^{6} x^{11}}{11 b x +11 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (6 e^{4} a \,b^{5}+4 d \,e^{3} b^{6}\right ) x^{10}}{10 b x +10 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (15 e^{4} a^{2} b^{4}+24 d \,e^{3} a \,b^{5}+6 d^{2} e^{2} b^{6}\right ) x^{9}}{9 b x +9 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (20 e^{4} a^{3} b^{3}+60 d \,e^{3} a^{2} b^{4}+36 d^{2} e^{2} a \,b^{5}+4 d^{3} e \,b^{6}\right ) x^{8}}{8 b x +8 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (15 e^{4} a^{4} b^{2}+80 d \,e^{3} a^{3} b^{3}+90 d^{2} e^{2} a^{2} b^{4}+24 d^{3} e a \,b^{5}+d^{4} b^{6}\right ) x^{7}}{7 b x +7 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (6 e^{4} a^{5} b +60 d \,e^{3} a^{4} b^{2}+120 d^{2} e^{2} a^{3} b^{3}+60 d^{3} e \,a^{2} b^{4}+6 d^{4} a \,b^{5}\right ) x^{6}}{6 b x +6 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (e^{4} a^{6}+24 d \,e^{3} a^{5} b +90 d^{2} e^{2} a^{4} b^{2}+80 d^{3} e \,a^{3} b^{3}+15 d^{4} a^{2} b^{4}\right ) x^{5}}{5 b x +5 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (4 d \,e^{3} a^{6}+36 d^{2} e^{2} a^{5} b +60 d^{3} e \,a^{4} b^{2}+20 d^{4} a^{3} b^{3}\right ) x^{4}}{4 b x +4 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (6 d^{2} e^{2} a^{6}+24 d^{3} e \,a^{5} b +15 d^{4} a^{4} b^{2}\right ) x^{3}}{3 b x +3 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (4 d^{3} e \,a^{6}+6 d^{4} a^{5} b \right ) x^{2}}{2 b x +2 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, d^{4} a^{6} x}{b x +a}\) | \(603\) |
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. 972 vs.
\(2 (156) = 312\).
time = 0.29, size = 972, normalized size = 4.44 \begin {gather*} \frac {1}{6} \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a d^{4} x + \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a^{2} d^{4}}{6 \, b} + \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} x^{4} e^{4}}{11 \, b} - \frac {3 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} a x^{3} e^{4}}{22 \, b^{2}} + \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (4 \, b d e^{3} + a e^{4}\right )} x^{3}}{10 \, b^{2}} - \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a^{5} x e^{4}}{6 \, b^{4}} + \frac {31 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} a^{2} x^{2} e^{4}}{198 \, b^{3}} + \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} {\left (4 \, b d e^{3} + a e^{4}\right )} a^{4} x}{6 \, b^{4}} - \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} {\left (3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right )} a^{3} x}{3 \, b^{3}} + \frac {{\left (2 \, b d^{3} e + 3 \, a d^{2} e^{2}\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a^{2} x}{3 \, b^{2}} - \frac {{\left (b d^{4} + 4 \, a d^{3} e\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a x}{6 \, b} - \frac {13 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (4 \, b d e^{3} + a e^{4}\right )} a x^{2}}{90 \, b^{3}} + \frac {2 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right )} x^{2}}{9 \, b^{2}} - \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a^{6} e^{4}}{6 \, b^{5}} - \frac {65 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} a^{3} x e^{4}}{396 \, b^{4}} + \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} {\left (4 \, b d e^{3} + a e^{4}\right )} a^{5}}{6 \, b^{5}} - \frac {{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} {\left (3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right )} a^{4}}{3 \, b^{4}} + \frac {{\left (2 \, b d^{3} e + 3 \, a d^{2} e^{2}\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a^{3}}{3 \, b^{3}} - \frac {{\left (b d^{4} + 4 \, a d^{3} e\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {5}{2}} a^{2}}{6 \, b^{2}} + \frac {29 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (4 \, b d e^{3} + a e^{4}\right )} a^{2} x}{180 \, b^{4}} - \frac {11 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right )} a x}{36 \, b^{3}} + \frac {{\left (2 \, b d^{3} e + 3 \, a d^{2} e^{2}\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} x}{4 \, b^{2}} + \frac {461 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} a^{4} e^{4}}{2772 \, b^{5}} - \frac {209 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (4 \, b d e^{3} + a e^{4}\right )} a^{3}}{1260 \, b^{5}} + \frac {83 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} {\left (3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right )} a^{2}}{252 \, b^{4}} - \frac {9 \, {\left (2 \, b d^{3} e + 3 \, a d^{2} e^{2}\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}} a}{28 \, b^{3}} + \frac {{\left (b d^{4} + 4 \, a d^{3} e\right )} {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{\frac {7}{2}}}{7 \, b^{2}} \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. 422 vs.
\(2 (156) = 312\).
time = 2.20, size = 422, normalized size = 1.93 \begin {gather*} \frac {1}{7} \, b^{6} d^{4} x^{7} + a b^{5} d^{4} x^{6} + 3 \, a^{2} b^{4} d^{4} x^{5} + 5 \, a^{3} b^{3} d^{4} x^{4} + 5 \, a^{4} b^{2} d^{4} x^{3} + 3 \, a^{5} b d^{4} x^{2} + a^{6} d^{4} x + \frac {1}{2310} \, {\left (210 \, b^{6} x^{11} + 1386 \, a b^{5} x^{10} + 3850 \, a^{2} b^{4} x^{9} + 5775 \, a^{3} b^{3} x^{8} + 4950 \, a^{4} b^{2} x^{7} + 2310 \, a^{5} b x^{6} + 462 \, a^{6} x^{5}\right )} e^{4} + \frac {1}{210} \, {\left (84 \, b^{6} d x^{10} + 560 \, a b^{5} d x^{9} + 1575 \, a^{2} b^{4} d x^{8} + 2400 \, a^{3} b^{3} d x^{7} + 2100 \, a^{4} b^{2} d x^{6} + 1008 \, a^{5} b d x^{5} + 210 \, a^{6} d x^{4}\right )} e^{3} + \frac {1}{42} \, {\left (28 \, b^{6} d^{2} x^{9} + 189 \, a b^{5} d^{2} x^{8} + 540 \, a^{2} b^{4} d^{2} x^{7} + 840 \, a^{3} b^{3} d^{2} x^{6} + 756 \, a^{4} b^{2} d^{2} x^{5} + 378 \, a^{5} b d^{2} x^{4} + 84 \, a^{6} d^{2} x^{3}\right )} e^{2} + \frac {1}{14} \, {\left (7 \, b^{6} d^{3} x^{8} + 48 \, a b^{5} d^{3} x^{7} + 140 \, a^{2} b^{4} d^{3} x^{6} + 224 \, a^{3} b^{3} d^{3} x^{5} + 210 \, a^{4} b^{2} d^{3} x^{4} + 112 \, a^{5} b d^{3} x^{3} + 28 \, a^{6} d^{3} x^{2}\right )} e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a + b x\right ) \left (d + e x\right )^{4} \left (\left (a + b x\right )^{2}\right )^{\frac {5}{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 666 vs.
\(2 (156) = 312\).
time = 1.28, size = 666, normalized size = 3.04 \begin {gather*} \frac {1}{11} \, b^{6} x^{11} e^{4} \mathrm {sgn}\left (b x + a\right ) + \frac {2}{5} \, b^{6} d x^{10} e^{3} \mathrm {sgn}\left (b x + a\right ) + \frac {2}{3} \, b^{6} d^{2} x^{9} e^{2} \mathrm {sgn}\left (b x + a\right ) + \frac {1}{2} \, b^{6} d^{3} x^{8} e \mathrm {sgn}\left (b x + a\right ) + \frac {1}{7} \, b^{6} d^{4} x^{7} \mathrm {sgn}\left (b x + a\right ) + \frac {3}{5} \, a b^{5} x^{10} e^{4} \mathrm {sgn}\left (b x + a\right ) + \frac {8}{3} \, a b^{5} d x^{9} e^{3} \mathrm {sgn}\left (b x + a\right ) + \frac {9}{2} \, a b^{5} d^{2} x^{8} e^{2} \mathrm {sgn}\left (b x + a\right ) + \frac {24}{7} \, a b^{5} d^{3} x^{7} e \mathrm {sgn}\left (b x + a\right ) + a b^{5} d^{4} x^{6} \mathrm {sgn}\left (b x + a\right ) + \frac {5}{3} \, a^{2} b^{4} x^{9} e^{4} \mathrm {sgn}\left (b x + a\right ) + \frac {15}{2} \, a^{2} b^{4} d x^{8} e^{3} \mathrm {sgn}\left (b x + a\right ) + \frac {90}{7} \, a^{2} b^{4} d^{2} x^{7} e^{2} \mathrm {sgn}\left (b x + a\right ) + 10 \, a^{2} b^{4} d^{3} x^{6} e \mathrm {sgn}\left (b x + a\right ) + 3 \, a^{2} b^{4} d^{4} x^{5} \mathrm {sgn}\left (b x + a\right ) + \frac {5}{2} \, a^{3} b^{3} x^{8} e^{4} \mathrm {sgn}\left (b x + a\right ) + \frac {80}{7} \, a^{3} b^{3} d x^{7} e^{3} \mathrm {sgn}\left (b x + a\right ) + 20 \, a^{3} b^{3} d^{2} x^{6} e^{2} \mathrm {sgn}\left (b x + a\right ) + 16 \, a^{3} b^{3} d^{3} x^{5} e \mathrm {sgn}\left (b x + a\right ) + 5 \, a^{3} b^{3} d^{4} x^{4} \mathrm {sgn}\left (b x + a\right ) + \frac {15}{7} \, a^{4} b^{2} x^{7} e^{4} \mathrm {sgn}\left (b x + a\right ) + 10 \, a^{4} b^{2} d x^{6} e^{3} \mathrm {sgn}\left (b x + a\right ) + 18 \, a^{4} b^{2} d^{2} x^{5} e^{2} \mathrm {sgn}\left (b x + a\right ) + 15 \, a^{4} b^{2} d^{3} x^{4} e \mathrm {sgn}\left (b x + a\right ) + 5 \, a^{4} b^{2} d^{4} x^{3} \mathrm {sgn}\left (b x + a\right ) + a^{5} b x^{6} e^{4} \mathrm {sgn}\left (b x + a\right ) + \frac {24}{5} \, a^{5} b d x^{5} e^{3} \mathrm {sgn}\left (b x + a\right ) + 9 \, a^{5} b d^{2} x^{4} e^{2} \mathrm {sgn}\left (b x + a\right ) + 8 \, a^{5} b d^{3} x^{3} e \mathrm {sgn}\left (b x + a\right ) + 3 \, a^{5} b d^{4} x^{2} \mathrm {sgn}\left (b x + a\right ) + \frac {1}{5} \, a^{6} x^{5} e^{4} \mathrm {sgn}\left (b x + a\right ) + a^{6} d x^{4} e^{3} \mathrm {sgn}\left (b x + a\right ) + 2 \, a^{6} d^{2} x^{3} e^{2} \mathrm {sgn}\left (b x + a\right ) + 2 \, a^{6} d^{3} x^{2} e \mathrm {sgn}\left (b x + a\right ) + a^{6} d^{4} x \mathrm {sgn}\left (b x + a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \left (a+b\,x\right )\,{\left (d+e\,x\right )}^4\,{\left (a^2+2\,a\,b\,x+b^2\,x^2\right )}^{5/2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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