Optimal. Leaf size=83 \[ 2 A b^3 \sqrt{x}+\frac{2}{3} b^2 x^{3/2} (3 A c+b B)+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{6}{5} b c x^{5/2} (A c+b B)+\frac{2}{9} B c^3 x^{9/2} \]
[Out]
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Rubi [A] time = 0.120045, antiderivative size = 83, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ 2 A b^3 \sqrt{x}+\frac{2}{3} b^2 x^{3/2} (3 A c+b B)+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{6}{5} b c x^{5/2} (A c+b B)+\frac{2}{9} B c^3 x^{9/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 13.7748, size = 82, normalized size = 0.99 \[ 2 A b^{3} \sqrt{x} + \frac{2 B c^{3} x^{\frac{9}{2}}}{9} + 2 b^{2} x^{\frac{3}{2}} \left (A c + \frac{B b}{3}\right ) + \frac{6 b c x^{\frac{5}{2}} \left (A c + B b\right )}{5} + \frac{2 c^{2} x^{\frac{7}{2}} \left (A c + 3 B b\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0401191, size = 69, normalized size = 0.83 \[ \frac{2}{315} \sqrt{x} \left (315 A b^3+105 b^2 x (3 A c+b B)+45 c^2 x^3 (A c+3 b B)+189 b c x^2 (A c+b B)+35 B c^3 x^4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(7/2),x]
[Out]
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Maple [A] time = 0.009, size = 76, normalized size = 0.9 \[{\frac{70\,B{c}^{3}{x}^{4}+90\,A{c}^{3}{x}^{3}+270\,B{x}^{3}b{c}^{2}+378\,Ab{c}^{2}{x}^{2}+378\,B{x}^{2}{b}^{2}c+630\,A{b}^{2}cx+210\,Bx{b}^{3}+630\,A{b}^{3}}{315}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^(7/2),x)
[Out]
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Maxima [A] time = 0.683821, size = 99, normalized size = 1.19 \[ \frac{2}{9} \, B c^{3} x^{\frac{9}{2}} + 2 \, A b^{3} \sqrt{x} + \frac{2}{7} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{\frac{7}{2}} + \frac{6}{5} \,{\left (B b^{2} c + A b c^{2}\right )} x^{\frac{5}{2}} + \frac{2}{3} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269291, size = 99, normalized size = 1.19 \[ \frac{2}{315} \,{\left (35 \, B c^{3} x^{4} + 315 \, A b^{3} + 45 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 189 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 105 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 17.3269, size = 110, normalized size = 1.33 \[ 2 A b^{3} \sqrt{x} + 2 A b^{2} c x^{\frac{3}{2}} + \frac{6 A b c^{2} x^{\frac{5}{2}}}{5} + \frac{2 A c^{3} x^{\frac{7}{2}}}{7} + \frac{2 B b^{3} x^{\frac{3}{2}}}{3} + \frac{6 B b^{2} c x^{\frac{5}{2}}}{5} + \frac{6 B b c^{2} x^{\frac{7}{2}}}{7} + \frac{2 B c^{3} x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.268607, size = 104, normalized size = 1.25 \[ \frac{2}{9} \, B c^{3} x^{\frac{9}{2}} + \frac{6}{7} \, B b c^{2} x^{\frac{7}{2}} + \frac{2}{7} \, A c^{3} x^{\frac{7}{2}} + \frac{6}{5} \, B b^{2} c x^{\frac{5}{2}} + \frac{6}{5} \, A b c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, B b^{3} x^{\frac{3}{2}} + 2 \, A b^{2} c x^{\frac{3}{2}} + 2 \, A b^{3} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^(7/2),x, algorithm="giac")
[Out]