Optimal. Leaf size=110 \[ -\frac{2 a^5 (a+b x)^{11/2}}{11 b^6}+\frac{10 a^4 (a+b x)^{13/2}}{13 b^6}-\frac{4 a^3 (a+b x)^{15/2}}{3 b^6}+\frac{20 a^2 (a+b x)^{17/2}}{17 b^6}+\frac{2 (a+b x)^{21/2}}{21 b^6}-\frac{10 a (a+b x)^{19/2}}{19 b^6} \]
[Out]
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Rubi [A] time = 0.0786845, antiderivative size = 110, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{2 a^5 (a+b x)^{11/2}}{11 b^6}+\frac{10 a^4 (a+b x)^{13/2}}{13 b^6}-\frac{4 a^3 (a+b x)^{15/2}}{3 b^6}+\frac{20 a^2 (a+b x)^{17/2}}{17 b^6}+\frac{2 (a+b x)^{21/2}}{21 b^6}-\frac{10 a (a+b x)^{19/2}}{19 b^6} \]
Antiderivative was successfully verified.
[In] Int[x^5*(a + b*x)^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 17.7991, size = 105, normalized size = 0.95 \[ - \frac{2 a^{5} \left (a + b x\right )^{\frac{11}{2}}}{11 b^{6}} + \frac{10 a^{4} \left (a + b x\right )^{\frac{13}{2}}}{13 b^{6}} - \frac{4 a^{3} \left (a + b x\right )^{\frac{15}{2}}}{3 b^{6}} + \frac{20 a^{2} \left (a + b x\right )^{\frac{17}{2}}}{17 b^{6}} - \frac{10 a \left (a + b x\right )^{\frac{19}{2}}}{19 b^{6}} + \frac{2 \left (a + b x\right )^{\frac{21}{2}}}{21 b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5*(b*x+a)**(9/2),x)
[Out]
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Mathematica [A] time = 0.0572699, size = 68, normalized size = 0.62 \[ \frac{2 (a+b x)^{11/2} \left (-256 a^5+1408 a^4 b x-4576 a^3 b^2 x^2+11440 a^2 b^3 x^3-24310 a b^4 x^4+46189 b^5 x^5\right )}{969969 b^6} \]
Antiderivative was successfully verified.
[In] Integrate[x^5*(a + b*x)^(9/2),x]
[Out]
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Maple [A] time = 0.009, size = 65, normalized size = 0.6 \[ -{\frac{-92378\,{b}^{5}{x}^{5}+48620\,a{b}^{4}{x}^{4}-22880\,{a}^{2}{b}^{3}{x}^{3}+9152\,{a}^{3}{b}^{2}{x}^{2}-2816\,{a}^{4}bx+512\,{a}^{5}}{969969\,{b}^{6}} \left ( bx+a \right ) ^{{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5*(b*x+a)^(9/2),x)
[Out]
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Maxima [A] time = 1.34494, size = 116, normalized size = 1.05 \[ \frac{2 \,{\left (b x + a\right )}^{\frac{21}{2}}}{21 \, b^{6}} - \frac{10 \,{\left (b x + a\right )}^{\frac{19}{2}} a}{19 \, b^{6}} + \frac{20 \,{\left (b x + a\right )}^{\frac{17}{2}} a^{2}}{17 \, b^{6}} - \frac{4 \,{\left (b x + a\right )}^{\frac{15}{2}} a^{3}}{3 \, b^{6}} + \frac{10 \,{\left (b x + a\right )}^{\frac{13}{2}} a^{4}}{13 \, b^{6}} - \frac{2 \,{\left (b x + a\right )}^{\frac{11}{2}} a^{5}}{11 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(9/2)*x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208456, size = 161, normalized size = 1.46 \[ \frac{2 \,{\left (46189 \, b^{10} x^{10} + 206635 \, a b^{9} x^{9} + 351780 \, a^{2} b^{8} x^{8} + 271414 \, a^{3} b^{7} x^{7} + 80773 \, a^{4} b^{6} x^{6} + 63 \, a^{5} b^{5} x^{5} - 70 \, a^{6} b^{4} x^{4} + 80 \, a^{7} b^{3} x^{3} - 96 \, a^{8} b^{2} x^{2} + 128 \, a^{9} b x - 256 \, a^{10}\right )} \sqrt{b x + a}}{969969 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(9/2)*x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 82.6622, size = 235, normalized size = 2.14 \[ \begin{cases} - \frac{512 a^{10} \sqrt{a + b x}}{969969 b^{6}} + \frac{256 a^{9} x \sqrt{a + b x}}{969969 b^{5}} - \frac{64 a^{8} x^{2} \sqrt{a + b x}}{323323 b^{4}} + \frac{160 a^{7} x^{3} \sqrt{a + b x}}{969969 b^{3}} - \frac{20 a^{6} x^{4} \sqrt{a + b x}}{138567 b^{2}} + \frac{6 a^{5} x^{5} \sqrt{a + b x}}{46189 b} + \frac{2098 a^{4} x^{6} \sqrt{a + b x}}{12597} + \frac{3796 a^{3} b x^{7} \sqrt{a + b x}}{6783} + \frac{1640 a^{2} b^{2} x^{8} \sqrt{a + b x}}{2261} + \frac{170 a b^{3} x^{9} \sqrt{a + b x}}{399} + \frac{2 b^{4} x^{10} \sqrt{a + b x}}{21} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{6}}{6} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5*(b*x+a)**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215117, size = 1, normalized size = 0.01 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(9/2)*x^5,x, algorithm="giac")
[Out]