Optimal. Leaf size=140 \[ \frac{256 b^5 \left (a+b x^2\right )^{7/2}}{153153 a^6 x^7}-\frac{128 b^4 \left (a+b x^2\right )^{7/2}}{21879 a^5 x^9}+\frac{32 b^3 \left (a+b x^2\right )^{7/2}}{2431 a^4 x^{11}}-\frac{16 b^2 \left (a+b x^2\right )^{7/2}}{663 a^3 x^{13}}+\frac{2 b \left (a+b x^2\right )^{7/2}}{51 a^2 x^{15}}-\frac{\left (a+b x^2\right )^{7/2}}{17 a x^{17}} \]
[Out]
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Rubi [A] time = 0.171818, antiderivative size = 140, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{256 b^5 \left (a+b x^2\right )^{7/2}}{153153 a^6 x^7}-\frac{128 b^4 \left (a+b x^2\right )^{7/2}}{21879 a^5 x^9}+\frac{32 b^3 \left (a+b x^2\right )^{7/2}}{2431 a^4 x^{11}}-\frac{16 b^2 \left (a+b x^2\right )^{7/2}}{663 a^3 x^{13}}+\frac{2 b \left (a+b x^2\right )^{7/2}}{51 a^2 x^{15}}-\frac{\left (a+b x^2\right )^{7/2}}{17 a x^{17}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^(5/2)/x^18,x]
[Out]
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Rubi in Sympy [A] time = 20.9123, size = 133, normalized size = 0.95 \[ - \frac{\left (a + b x^{2}\right )^{\frac{7}{2}}}{17 a x^{17}} + \frac{2 b \left (a + b x^{2}\right )^{\frac{7}{2}}}{51 a^{2} x^{15}} - \frac{16 b^{2} \left (a + b x^{2}\right )^{\frac{7}{2}}}{663 a^{3} x^{13}} + \frac{32 b^{3} \left (a + b x^{2}\right )^{\frac{7}{2}}}{2431 a^{4} x^{11}} - \frac{128 b^{4} \left (a + b x^{2}\right )^{\frac{7}{2}}}{21879 a^{5} x^{9}} + \frac{256 b^{5} \left (a + b x^{2}\right )^{\frac{7}{2}}}{153153 a^{6} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**(5/2)/x**18,x)
[Out]
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Mathematica [A] time = 0.0690831, size = 75, normalized size = 0.54 \[ \frac{\left (a+b x^2\right )^{7/2} \left (-9009 a^5+6006 a^4 b x^2-3696 a^3 b^2 x^4+2016 a^2 b^3 x^6-896 a b^4 x^8+256 b^5 x^{10}\right )}{153153 a^6 x^{17}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^(5/2)/x^18,x]
[Out]
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Maple [A] time = 0.009, size = 72, normalized size = 0.5 \[ -{\frac{-256\,{b}^{5}{x}^{10}+896\,a{b}^{4}{x}^{8}-2016\,{a}^{2}{b}^{3}{x}^{6}+3696\,{a}^{3}{b}^{2}{x}^{4}-6006\,{a}^{4}b{x}^{2}+9009\,{a}^{5}}{153153\,{x}^{17}{a}^{6}} \left ( b{x}^{2}+a \right ) ^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^(5/2)/x^18,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^2 + a)^(5/2)/x^18,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.767374, size = 140, normalized size = 1. \[ \frac{{\left (256 \, b^{8} x^{16} - 128 \, a b^{7} x^{14} + 96 \, a^{2} b^{6} x^{12} - 80 \, a^{3} b^{5} x^{10} + 70 \, a^{4} b^{4} x^{8} - 63 \, a^{5} b^{3} x^{6} - 12705 \, a^{6} b^{2} x^{4} - 21021 \, a^{7} b x^{2} - 9009 \, a^{8}\right )} \sqrt{b x^{2} + a}}{153153 \, a^{6} x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(5/2)/x^18,x, algorithm="fricas")
[Out]
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Sympy [A] time = 39.243, size = 1346, normalized size = 9.61 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**(5/2)/x**18,x)
[Out]
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GIAC/XCAS [A] time = 0.214715, size = 443, normalized size = 3.16 \[ \frac{512 \,{\left (102102 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{22} b^{\frac{17}{2}} + 364650 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{20} a b^{\frac{17}{2}} + 692835 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{18} a^{2} b^{\frac{17}{2}} + 668525 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{16} a^{3} b^{\frac{17}{2}} + 384098 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{14} a^{4} b^{\frac{17}{2}} + 89726 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{12} a^{5} b^{\frac{17}{2}} + 6188 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{10} a^{6} b^{\frac{17}{2}} - 2380 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{8} a^{7} b^{\frac{17}{2}} + 680 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{6} a^{8} b^{\frac{17}{2}} - 136 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{4} a^{9} b^{\frac{17}{2}} + 17 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{2} a^{10} b^{\frac{17}{2}} - a^{11} b^{\frac{17}{2}}\right )}}{153153 \,{\left ({\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{2} - a\right )}^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(5/2)/x^18,x, algorithm="giac")
[Out]