Optimal. Leaf size=81 \[ -\frac{2 A b^3}{3 x^{3/2}}-\frac{2 b^2 (3 A c+b B)}{\sqrt{x}}+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+6 b c \sqrt{x} (A c+b B)+\frac{2}{5} B c^3 x^{5/2} \]
[Out]
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Rubi [A] time = 0.123039, antiderivative size = 81, 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 \[ -\frac{2 A b^3}{3 x^{3/2}}-\frac{2 b^2 (3 A c+b B)}{\sqrt{x}}+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+6 b c \sqrt{x} (A c+b B)+\frac{2}{5} B c^3 x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x^(11/2),x]
[Out]
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Rubi in Sympy [A] time = 13.8564, size = 80, normalized size = 0.99 \[ - \frac{2 A b^{3}}{3 x^{\frac{3}{2}}} + \frac{2 B c^{3} x^{\frac{5}{2}}}{5} - \frac{2 b^{2} \left (3 A c + B b\right )}{\sqrt{x}} + 6 b c \sqrt{x} \left (A c + B b\right ) + 2 c^{2} x^{\frac{3}{2}} \left (\frac{A c}{3} + B b\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**(11/2),x)
[Out]
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Mathematica [A] time = 0.0370505, size = 74, normalized size = 0.91 \[ \frac{6 B x \left (-5 b^3+15 b^2 c x+5 b c^2 x^2+c^3 x^3\right )-10 A \left (b^3+9 b^2 c x-9 b c^2 x^2-c^3 x^3\right )}{15 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^(11/2),x]
[Out]
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Maple [A] time = 0.008, size = 76, normalized size = 0.9 \[ -{\frac{-6\,B{c}^{3}{x}^{4}-10\,A{c}^{3}{x}^{3}-30\,B{x}^{3}b{c}^{2}-90\,Ab{c}^{2}{x}^{2}-90\,B{x}^{2}{b}^{2}c+90\,A{b}^{2}cx+30\,Bx{b}^{3}+10\,A{b}^{3}}{15}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^(11/2),x)
[Out]
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Maxima [A] time = 0.683247, size = 99, normalized size = 1.22 \[ \frac{2}{5} \, B c^{3} x^{\frac{5}{2}} + \frac{2}{3} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{\frac{3}{2}} + 6 \,{\left (B b^{2} c + A b c^{2}\right )} \sqrt{x} - \frac{2 \,{\left (A b^{3} + 3 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^(11/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.278044, size = 99, normalized size = 1.22 \[ \frac{2 \,{\left (3 \, B c^{3} x^{4} - 5 \, A b^{3} + 5 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 45 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} - 15 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x\right )}}{15 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^(11/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 32.1663, size = 105, normalized size = 1.3 \[ - \frac{2 A b^{3}}{3 x^{\frac{3}{2}}} - \frac{6 A b^{2} c}{\sqrt{x}} + 6 A b c^{2} \sqrt{x} + \frac{2 A c^{3} x^{\frac{3}{2}}}{3} - \frac{2 B b^{3}}{\sqrt{x}} + 6 B b^{2} c \sqrt{x} + 2 B b c^{2} x^{\frac{3}{2}} + \frac{2 B c^{3} x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**(11/2),x)
[Out]
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GIAC/XCAS [A] time = 0.268123, size = 101, normalized size = 1.25 \[ \frac{2}{5} \, B c^{3} x^{\frac{5}{2}} + 2 \, B b c^{2} x^{\frac{3}{2}} + \frac{2}{3} \, A c^{3} x^{\frac{3}{2}} + 6 \, B b^{2} c \sqrt{x} + 6 \, A b c^{2} \sqrt{x} - \frac{2 \,{\left (3 \, B b^{3} x + 9 \, A b^{2} c x + A b^{3}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^(11/2),x, algorithm="giac")
[Out]