Optimal. Leaf size=40 \[ \frac{\left (a-b x^4\right )^{9/4}}{9 b^2}-\frac{a \left (a-b x^4\right )^{5/4}}{5 b^2} \]
[Out]
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Rubi [A] time = 0.0608294, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{\left (a-b x^4\right )^{9/4}}{9 b^2}-\frac{a \left (a-b x^4\right )^{5/4}}{5 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^7*(a - b*x^4)^(1/4),x]
[Out]
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Rubi in Sympy [A] time = 7.87063, size = 31, normalized size = 0.78 \[ - \frac{a \left (a - b x^{4}\right )^{\frac{5}{4}}}{5 b^{2}} + \frac{\left (a - b x^{4}\right )^{\frac{9}{4}}}{9 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7*(-b*x**4+a)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0243849, size = 29, normalized size = 0.72 \[ -\frac{\left (a-b x^4\right )^{5/4} \left (4 a+5 b x^4\right )}{45 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^7*(a - b*x^4)^(1/4),x]
[Out]
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Maple [A] time = 0.007, size = 26, normalized size = 0.7 \[ -{\frac{5\,b{x}^{4}+4\,a}{45\,{b}^{2}} \left ( -b{x}^{4}+a \right ) ^{{\frac{5}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7*(-b*x^4+a)^(1/4),x)
[Out]
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Maxima [A] time = 1.46569, size = 43, normalized size = 1.08 \[ \frac{{\left (-b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, b^{2}} - \frac{{\left (-b x^{4} + a\right )}^{\frac{5}{4}} a}{5 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)*x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.243353, size = 49, normalized size = 1.22 \[ \frac{{\left (5 \, b^{2} x^{8} - a b x^{4} - 4 \, a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{45 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)*x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.31396, size = 63, normalized size = 1.58 \[ \begin{cases} - \frac{4 a^{2} \sqrt [4]{a - b x^{4}}}{45 b^{2}} - \frac{a x^{4} \sqrt [4]{a - b x^{4}}}{45 b} + \frac{x^{8} \sqrt [4]{a - b x^{4}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt [4]{a} x^{8}}{8} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7*(-b*x**4+a)**(1/4),x)
[Out]
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GIAC/XCAS [A] time = 0.250776, size = 57, normalized size = 1.42 \[ \frac{5 \,{\left (b x^{4} - a\right )}^{2}{\left (-b x^{4} + a\right )}^{\frac{1}{4}} - 9 \,{\left (-b x^{4} + a\right )}^{\frac{5}{4}} a}{45 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*x^4 + a)^(1/4)*x^7,x, algorithm="giac")
[Out]