Optimal. Leaf size=68 \[ -\frac{4 c^2 \left (a+c x^4\right )^{5/2}}{315 a^3 x^{10}}+\frac{2 c \left (a+c x^4\right )^{5/2}}{63 a^2 x^{14}}-\frac{\left (a+c x^4\right )^{5/2}}{18 a x^{18}} \]
[Out]
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Rubi [A] time = 0.0638984, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{4 c^2 \left (a+c x^4\right )^{5/2}}{315 a^3 x^{10}}+\frac{2 c \left (a+c x^4\right )^{5/2}}{63 a^2 x^{14}}-\frac{\left (a+c x^4\right )^{5/2}}{18 a x^{18}} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^(3/2)/x^19,x]
[Out]
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Rubi in Sympy [A] time = 6.68596, size = 61, normalized size = 0.9 \[ - \frac{\left (a + c x^{4}\right )^{\frac{5}{2}}}{18 a x^{18}} + \frac{2 c \left (a + c x^{4}\right )^{\frac{5}{2}}}{63 a^{2} x^{14}} - \frac{4 c^{2} \left (a + c x^{4}\right )^{\frac{5}{2}}}{315 a^{3} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**(3/2)/x**19,x)
[Out]
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Mathematica [A] time = 0.0539661, size = 42, normalized size = 0.62 \[ -\frac{\left (a+c x^4\right )^{5/2} \left (35 a^2-20 a c x^4+8 c^2 x^8\right )}{630 a^3 x^{18}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^(3/2)/x^19,x]
[Out]
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Maple [A] time = 0.008, size = 39, normalized size = 0.6 \[ -{\frac{8\,{c}^{2}{x}^{8}-20\,c{x}^{4}a+35\,{a}^{2}}{630\,{x}^{18}{a}^{3}} \left ( c{x}^{4}+a \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^(3/2)/x^19,x)
[Out]
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Maxima [A] time = 1.43231, size = 70, normalized size = 1.03 \[ -\frac{\frac{63 \,{\left (c x^{4} + a\right )}^{\frac{5}{2}} c^{2}}{x^{10}} - \frac{90 \,{\left (c x^{4} + a\right )}^{\frac{7}{2}} c}{x^{14}} + \frac{35 \,{\left (c x^{4} + a\right )}^{\frac{9}{2}}}{x^{18}}}{630 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^(3/2)/x^19,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.318325, size = 81, normalized size = 1.19 \[ -\frac{{\left (8 \, c^{4} x^{16} - 4 \, a c^{3} x^{12} + 3 \, a^{2} c^{2} x^{8} + 50 \, a^{3} c x^{4} + 35 \, a^{4}\right )} \sqrt{c x^{4} + a}}{630 \, a^{3} x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^(3/2)/x^19,x, algorithm="fricas")
[Out]
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Sympy [A] time = 32.2862, size = 420, normalized size = 6.18 \[ - \frac{35 a^{6} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{120 a^{5} c^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{138 a^{4} c^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{52 a^{3} c^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{3 a^{2} c^{\frac{17}{2}} x^{16} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{12 a c^{\frac{19}{2}} x^{20} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} - \frac{8 c^{\frac{21}{2}} x^{24} \sqrt{\frac{a}{c x^{4}} + 1}}{630 a^{5} c^{4} x^{16} + 1260 a^{4} c^{5} x^{20} + 630 a^{3} c^{6} x^{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**(3/2)/x**19,x)
[Out]
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GIAC/XCAS [A] time = 0.217465, size = 143, normalized size = 2.1 \[ -\frac{\frac{3 \,{\left (15 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{7}{2}} - 42 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{5}{2}} c + 35 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} c^{2}\right )} c}{a^{2}} + \frac{35 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{9}{2}} - 135 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{7}{2}} c + 189 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{5}{2}} c^{2} - 105 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} c^{3}}{a^{2}}}{630 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^(3/2)/x^19,x, algorithm="giac")
[Out]