Optimal. Leaf size=127 \[ \frac{2 a^6 (a+b x)^{11/2}}{11 b^7}-\frac{12 a^5 (a+b x)^{13/2}}{13 b^7}+\frac{2 a^4 (a+b x)^{15/2}}{b^7}-\frac{40 a^3 (a+b x)^{17/2}}{17 b^7}+\frac{30 a^2 (a+b x)^{19/2}}{19 b^7}+\frac{2 (a+b x)^{23/2}}{23 b^7}-\frac{4 a (a+b x)^{21/2}}{7 b^7} \]
[Out]
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Rubi [A] time = 0.0898762, antiderivative size = 127, 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 \[ \frac{2 a^6 (a+b x)^{11/2}}{11 b^7}-\frac{12 a^5 (a+b x)^{13/2}}{13 b^7}+\frac{2 a^4 (a+b x)^{15/2}}{b^7}-\frac{40 a^3 (a+b x)^{17/2}}{17 b^7}+\frac{30 a^2 (a+b x)^{19/2}}{19 b^7}+\frac{2 (a+b x)^{23/2}}{23 b^7}-\frac{4 a (a+b x)^{21/2}}{7 b^7} \]
Antiderivative was successfully verified.
[In] Int[x^6*(a + b*x)^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 20.8355, size = 122, normalized size = 0.96 \[ \frac{2 a^{6} \left (a + b x\right )^{\frac{11}{2}}}{11 b^{7}} - \frac{12 a^{5} \left (a + b x\right )^{\frac{13}{2}}}{13 b^{7}} + \frac{2 a^{4} \left (a + b x\right )^{\frac{15}{2}}}{b^{7}} - \frac{40 a^{3} \left (a + b x\right )^{\frac{17}{2}}}{17 b^{7}} + \frac{30 a^{2} \left (a + b x\right )^{\frac{19}{2}}}{19 b^{7}} - \frac{4 a \left (a + b x\right )^{\frac{21}{2}}}{7 b^{7}} + \frac{2 \left (a + b x\right )^{\frac{23}{2}}}{23 b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**6*(b*x+a)**(9/2),x)
[Out]
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Mathematica [A] time = 0.0554012, size = 79, normalized size = 0.62 \[ \frac{2 (a+b x)^{11/2} \left (1024 a^6-5632 a^5 b x+18304 a^4 b^2 x^2-45760 a^3 b^3 x^3+97240 a^2 b^4 x^4-184756 a b^5 x^5+323323 b^6 x^6\right )}{7436429 b^7} \]
Antiderivative was successfully verified.
[In] Integrate[x^6*(a + b*x)^(9/2),x]
[Out]
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Maple [A] time = 0.01, size = 76, normalized size = 0.6 \[{\frac{646646\,{x}^{6}{b}^{6}-369512\,a{x}^{5}{b}^{5}+194480\,{a}^{2}{x}^{4}{b}^{4}-91520\,{a}^{3}{x}^{3}{b}^{3}+36608\,{a}^{4}{x}^{2}{b}^{2}-11264\,{a}^{5}xb+2048\,{a}^{6}}{7436429\,{b}^{7}} \left ( bx+a \right ) ^{{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^6*(b*x+a)^(9/2),x)
[Out]
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Maxima [A] time = 1.32669, size = 136, normalized size = 1.07 \[ \frac{2 \,{\left (b x + a\right )}^{\frac{23}{2}}}{23 \, b^{7}} - \frac{4 \,{\left (b x + a\right )}^{\frac{21}{2}} a}{7 \, b^{7}} + \frac{30 \,{\left (b x + a\right )}^{\frac{19}{2}} a^{2}}{19 \, b^{7}} - \frac{40 \,{\left (b x + a\right )}^{\frac{17}{2}} a^{3}}{17 \, b^{7}} + \frac{2 \,{\left (b x + a\right )}^{\frac{15}{2}} a^{4}}{b^{7}} - \frac{12 \,{\left (b x + a\right )}^{\frac{13}{2}} a^{5}}{13 \, b^{7}} + \frac{2 \,{\left (b x + a\right )}^{\frac{11}{2}} a^{6}}{11 \, b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(9/2)*x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206692, size = 176, normalized size = 1.39 \[ \frac{2 \,{\left (323323 \, b^{11} x^{11} + 1431859 \, a b^{10} x^{10} + 2406690 \, a^{2} b^{9} x^{9} + 1826110 \, a^{3} b^{8} x^{8} + 530959 \, a^{4} b^{7} x^{7} + 231 \, a^{5} b^{6} x^{6} - 252 \, a^{6} b^{5} x^{5} + 280 \, a^{7} b^{4} x^{4} - 320 \, a^{8} b^{3} x^{3} + 384 \, a^{9} b^{2} x^{2} - 512 \, a^{10} b x + 1024 \, a^{11}\right )} \sqrt{b x + a}}{7436429 \, b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(9/2)*x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 99.8002, size = 257, normalized size = 2.02 \[ \begin{cases} \frac{2048 a^{11} \sqrt{a + b x}}{7436429 b^{7}} - \frac{1024 a^{10} x \sqrt{a + b x}}{7436429 b^{6}} + \frac{768 a^{9} x^{2} \sqrt{a + b x}}{7436429 b^{5}} - \frac{640 a^{8} x^{3} \sqrt{a + b x}}{7436429 b^{4}} + \frac{80 a^{7} x^{4} \sqrt{a + b x}}{1062347 b^{3}} - \frac{72 a^{6} x^{5} \sqrt{a + b x}}{1062347 b^{2}} + \frac{6 a^{5} x^{6} \sqrt{a + b x}}{96577 b} + \frac{7426 a^{4} x^{7} \sqrt{a + b x}}{52003} + \frac{25540 a^{3} b x^{8} \sqrt{a + b x}}{52003} + \frac{1980 a^{2} b^{2} x^{9} \sqrt{a + b x}}{3059} + \frac{62 a b^{3} x^{10} \sqrt{a + b x}}{161} + \frac{2 b^{4} x^{11} \sqrt{a + b x}}{23} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{7}}{7} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**6*(b*x+a)**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214811, 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^6,x, algorithm="giac")
[Out]