Optimal. Leaf size=163 \[ \frac{b^2 (-3 a B e-A b e+4 b B d)}{6 e^5 (d+e x)^6}-\frac{3 b (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (d+e x)^7}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{8 e^5 (d+e x)^8}-\frac{(b d-a e)^3 (B d-A e)}{9 e^5 (d+e x)^9}-\frac{b^3 B}{5 e^5 (d+e x)^5} \]
[Out]
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Rubi [A] time = 0.360841, antiderivative size = 163, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{b^2 (-3 a B e-A b e+4 b B d)}{6 e^5 (d+e x)^6}-\frac{3 b (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (d+e x)^7}+\frac{(b d-a e)^2 (-a B e-3 A b e+4 b B d)}{8 e^5 (d+e x)^8}-\frac{(b d-a e)^3 (B d-A e)}{9 e^5 (d+e x)^9}-\frac{b^3 B}{5 e^5 (d+e x)^5} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^3*(A + B*x))/(d + e*x)^10,x]
[Out]
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Rubi in Sympy [A] time = 62.8212, size = 156, normalized size = 0.96 \[ - \frac{B b^{3}}{5 e^{5} \left (d + e x\right )^{5}} - \frac{b^{2} \left (A b e + 3 B a e - 4 B b d\right )}{6 e^{5} \left (d + e x\right )^{6}} - \frac{3 b \left (a e - b d\right ) \left (A b e + B a e - 2 B b d\right )}{7 e^{5} \left (d + e x\right )^{7}} - \frac{\left (a e - b d\right )^{2} \left (3 A b e + B a e - 4 B b d\right )}{8 e^{5} \left (d + e x\right )^{8}} - \frac{\left (A e - B d\right ) \left (a e - b d\right )^{3}}{9 e^{5} \left (d + e x\right )^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3*(B*x+A)/(e*x+d)**10,x)
[Out]
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Mathematica [A] time = 0.189841, size = 214, normalized size = 1.31 \[ -\frac{35 a^3 e^3 (8 A e+B (d+9 e x))+15 a^2 b e^2 \left (7 A e (d+9 e x)+2 B \left (d^2+9 d e x+36 e^2 x^2\right )\right )+15 a b^2 e \left (2 A e \left (d^2+9 d e x+36 e^2 x^2\right )+B \left (d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right )\right )+b^3 \left (5 A e \left (d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right )+4 B \left (d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right )\right )}{2520 e^5 (d+e x)^9} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^3*(A + B*x))/(d + e*x)^10,x]
[Out]
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Maple [A] time = 0.01, size = 281, normalized size = 1.7 \[ -{\frac{{a}^{3}A{e}^{4}-3\,A{a}^{2}bd{e}^{3}+3\,A{d}^{2}a{b}^{2}{e}^{2}-A{d}^{3}{b}^{3}e-B{a}^{3}d{e}^{3}+3\,B{d}^{2}{a}^{2}b{e}^{2}-3\,B{d}^{3}a{b}^{2}e+{b}^{3}B{d}^{4}}{9\,{e}^{5} \left ( ex+d \right ) ^{9}}}-{\frac{{b}^{2} \left ( Abe+3\,Bae-4\,Bbd \right ) }{6\,{e}^{5} \left ( ex+d \right ) ^{6}}}-{\frac{3\,A{a}^{2}b{e}^{3}-6\,Ada{b}^{2}{e}^{2}+3\,A{d}^{2}{b}^{3}e+B{a}^{3}{e}^{3}-6\,Bd{a}^{2}b{e}^{2}+9\,B{d}^{2}a{b}^{2}e-4\,{b}^{3}B{d}^{3}}{8\,{e}^{5} \left ( ex+d \right ) ^{8}}}-{\frac{3\,b \left ( Aab{e}^{2}-Ad{b}^{2}e+B{a}^{2}{e}^{2}-3\,Bdabe+2\,{b}^{2}B{d}^{2} \right ) }{7\,{e}^{5} \left ( ex+d \right ) ^{7}}}-{\frac{B{b}^{3}}{5\,{e}^{5} \left ( ex+d \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3*(B*x+A)/(e*x+d)^10,x)
[Out]
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Maxima [A] time = 1.43773, size = 478, normalized size = 2.93 \[ -\frac{504 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 280 \, A a^{3} e^{4} + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} d^{3} e + 30 \,{\left (B a^{2} b + A a b^{2}\right )} d^{2} e^{2} + 35 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} d e^{3} + 84 \,{\left (4 \, B b^{3} d e^{3} + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} e^{4}\right )} x^{3} + 36 \,{\left (4 \, B b^{3} d^{2} e^{2} + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} d e^{3} + 30 \,{\left (B a^{2} b + A a b^{2}\right )} e^{4}\right )} x^{2} + 9 \,{\left (4 \, B b^{3} d^{3} e + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} d^{2} e^{2} + 30 \,{\left (B a^{2} b + A a b^{2}\right )} d e^{3} + 35 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} e^{4}\right )} x}{2520 \,{\left (e^{14} x^{9} + 9 \, d e^{13} x^{8} + 36 \, d^{2} e^{12} x^{7} + 84 \, d^{3} e^{11} x^{6} + 126 \, d^{4} e^{10} x^{5} + 126 \, d^{5} e^{9} x^{4} + 84 \, d^{6} e^{8} x^{3} + 36 \, d^{7} e^{7} x^{2} + 9 \, d^{8} e^{6} x + d^{9} e^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/(e*x + d)^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209798, size = 478, normalized size = 2.93 \[ -\frac{504 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 280 \, A a^{3} e^{4} + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} d^{3} e + 30 \,{\left (B a^{2} b + A a b^{2}\right )} d^{2} e^{2} + 35 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} d e^{3} + 84 \,{\left (4 \, B b^{3} d e^{3} + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} e^{4}\right )} x^{3} + 36 \,{\left (4 \, B b^{3} d^{2} e^{2} + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} d e^{3} + 30 \,{\left (B a^{2} b + A a b^{2}\right )} e^{4}\right )} x^{2} + 9 \,{\left (4 \, B b^{3} d^{3} e + 5 \,{\left (3 \, B a b^{2} + A b^{3}\right )} d^{2} e^{2} + 30 \,{\left (B a^{2} b + A a b^{2}\right )} d e^{3} + 35 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} e^{4}\right )} x}{2520 \,{\left (e^{14} x^{9} + 9 \, d e^{13} x^{8} + 36 \, d^{2} e^{12} x^{7} + 84 \, d^{3} e^{11} x^{6} + 126 \, d^{4} e^{10} x^{5} + 126 \, d^{5} e^{9} x^{4} + 84 \, d^{6} e^{8} x^{3} + 36 \, d^{7} e^{7} x^{2} + 9 \, d^{8} e^{6} x + d^{9} e^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/(e*x + d)^10,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3*(B*x+A)/(e*x+d)**10,x)
[Out]
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GIAC/XCAS [A] time = 0.212314, size = 382, normalized size = 2.34 \[ -\frac{{\left (504 \, B b^{3} x^{4} e^{4} + 336 \, B b^{3} d x^{3} e^{3} + 144 \, B b^{3} d^{2} x^{2} e^{2} + 36 \, B b^{3} d^{3} x e + 4 \, B b^{3} d^{4} + 1260 \, B a b^{2} x^{3} e^{4} + 420 \, A b^{3} x^{3} e^{4} + 540 \, B a b^{2} d x^{2} e^{3} + 180 \, A b^{3} d x^{2} e^{3} + 135 \, B a b^{2} d^{2} x e^{2} + 45 \, A b^{3} d^{2} x e^{2} + 15 \, B a b^{2} d^{3} e + 5 \, A b^{3} d^{3} e + 1080 \, B a^{2} b x^{2} e^{4} + 1080 \, A a b^{2} x^{2} e^{4} + 270 \, B a^{2} b d x e^{3} + 270 \, A a b^{2} d x e^{3} + 30 \, B a^{2} b d^{2} e^{2} + 30 \, A a b^{2} d^{2} e^{2} + 315 \, B a^{3} x e^{4} + 945 \, A a^{2} b x e^{4} + 35 \, B a^{3} d e^{3} + 105 \, A a^{2} b d e^{3} + 280 \, A a^{3} e^{4}\right )} e^{\left (-5\right )}}{2520 \,{\left (x e + d\right )}^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/(e*x + d)^10,x, algorithm="giac")
[Out]