Optimal. Leaf size=42 \[ -\frac{4 b x}{3 a^2 \sqrt [4]{a+b x^4}}-\frac{1}{3 a x^3 \sqrt [4]{a+b x^4}} \]
[Out]
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Rubi [A] time = 0.0310998, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{4 b x}{3 a^2 \sqrt [4]{a+b x^4}}-\frac{1}{3 a x^3 \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(a + b*x^4)^(5/4)),x]
[Out]
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Rubi in Sympy [A] time = 3.51984, size = 39, normalized size = 0.93 \[ - \frac{1}{3 a x^{3} \sqrt [4]{a + b x^{4}}} - \frac{4 b x}{3 a^{2} \sqrt [4]{a + b x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(b*x**4+a)**(5/4),x)
[Out]
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Mathematica [A] time = 0.0267029, size = 29, normalized size = 0.69 \[ -\frac{a+4 b x^4}{3 a^2 x^3 \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(a + b*x^4)^(5/4)),x]
[Out]
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Maple [A] time = 0.007, size = 26, normalized size = 0.6 \[ -{\frac{4\,b{x}^{4}+a}{3\,{x}^{3}{a}^{2}}{\frac{1}{\sqrt [4]{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(b*x^4+a)^(5/4),x)
[Out]
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Maxima [A] time = 1.44252, size = 46, normalized size = 1.1 \[ -\frac{b x}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} a^{2}} - \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, a^{2} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(5/4)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.243377, size = 50, normalized size = 1.19 \[ -\frac{{\left (4 \, b x^{4} + a\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{3 \,{\left (a^{2} b x^{7} + a^{3} x^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(5/4)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.66138, size = 68, normalized size = 1.62 \[ \frac{\Gamma \left (- \frac{3}{4}\right )}{16 a \sqrt [4]{b} x^{4} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (\frac{5}{4}\right )} + \frac{b^{\frac{3}{4}} \Gamma \left (- \frac{3}{4}\right )}{4 a^{2} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (\frac{5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(b*x**4+a)**(5/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{5}{4}} x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(5/4)*x^4),x, algorithm="giac")
[Out]