Optimal. Leaf size=53 \[ \frac{2 (a+b x)^{7/2} (2 A b-9 a B)}{63 a^2 x^{7/2}}-\frac{2 A (a+b x)^{7/2}}{9 a x^{9/2}} \]
[Out]
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Rubi [A] time = 0.0654023, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{2 (a+b x)^{7/2} (2 A b-9 a B)}{63 a^2 x^{7/2}}-\frac{2 A (a+b x)^{7/2}}{9 a x^{9/2}} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^(5/2)*(A + B*x))/x^(11/2),x]
[Out]
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Rubi in Sympy [A] time = 5.31531, size = 49, normalized size = 0.92 \[ - \frac{2 A \left (a + b x\right )^{\frac{7}{2}}}{9 a x^{\frac{9}{2}}} + \frac{4 \left (a + b x\right )^{\frac{7}{2}} \left (A b - \frac{9 B a}{2}\right )}{63 a^{2} x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(5/2)*(B*x+A)/x**(11/2),x)
[Out]
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Mathematica [A] time = 0.0923177, size = 36, normalized size = 0.68 \[ -\frac{2 (a+b x)^{7/2} (7 a A+9 a B x-2 A b x)}{63 a^2 x^{9/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^(5/2)*(A + B*x))/x^(11/2),x]
[Out]
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Maple [A] time = 0.008, size = 31, normalized size = 0.6 \[ -{\frac{-4\,Abx+18\,Bax+14\,Aa}{63\,{a}^{2}} \left ( bx+a \right ) ^{{\frac{7}{2}}}{x}^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(5/2)*(B*x+A)/x^(11/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^(5/2)/x^(11/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230139, size = 132, normalized size = 2.49 \[ -\frac{2 \,{\left (7 \, A a^{4} +{\left (9 \, B a b^{3} - 2 \, A b^{4}\right )} x^{4} +{\left (27 \, B a^{2} b^{2} + A a b^{3}\right )} x^{3} + 3 \,{\left (9 \, B a^{3} b + 5 \, A a^{2} b^{2}\right )} x^{2} +{\left (9 \, B a^{4} + 19 \, A a^{3} b\right )} x\right )} \sqrt{b x + a}}{63 \, a^{2} x^{\frac{9}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^(5/2)/x^(11/2),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)**(5/2)*(B*x+A)/x**(11/2),x)
[Out]
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GIAC/XCAS [A] time = 0.246361, size = 116, normalized size = 2.19 \[ \frac{{\left (b x + a\right )}^{\frac{7}{2}} b{\left (\frac{{\left (9 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9}\right )}{\left (b x + a\right )}}{a^{5} b^{15}} - \frac{9 \,{\left (B a^{4} b^{8} - A a^{3} b^{9}\right )}}{a^{5} b^{15}}\right )}}{64512 \,{\left ({\left (b x + a\right )} b - a b\right )}^{\frac{9}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^(5/2)/x^(11/2),x, algorithm="giac")
[Out]