Optimal. Leaf size=92 \[ \frac{a (a+b x) \text{Gamma}\left (\frac{1}{3},-c \log (f) (a+b x)^3\right )}{3 b^2 \sqrt [3]{-c \log (f) (a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left (\frac{2}{3},-c \log (f) (a+b x)^3\right )}{3 b^2 \left (-c \log (f) (a+b x)^3\right )^{2/3}} \]
[Out]
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Rubi [A] time = 0.0930898, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{a (a+b x) \text{Gamma}\left (\frac{1}{3},-c \log (f) (a+b x)^3\right )}{3 b^2 \sqrt [3]{-c \log (f) (a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left (\frac{2}{3},-c \log (f) (a+b x)^3\right )}{3 b^2 \left (-c \log (f) (a+b x)^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[f^(c*(a + b*x)^3)*x,x]
[Out]
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Rubi in Sympy [A] time = 8.62724, size = 90, normalized size = 0.98 \[ \frac{a \left (a + b x\right ) \Gamma{\left (\frac{1}{3},- c \left (a + b x\right )^{3} \log{\left (f \right )} \right )}}{3 b^{2} \sqrt [3]{- c \left (a + b x\right )^{3} \log{\left (f \right )}}} - \frac{\left (a + b x\right )^{2} \Gamma{\left (\frac{2}{3},- c \left (a + b x\right )^{3} \log{\left (f \right )} \right )}}{3 b^{2} \left (- c \left (a + b x\right )^{3} \log{\left (f \right )}\right )^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(c*(b*x+a)**3)*x,x)
[Out]
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Mathematica [A] time = 0.555301, size = 0, normalized size = 0. \[ \int f^{c (a+b x)^3} x \, dx \]
Verification is Not applicable to the result.
[In] Integrate[f^(c*(a + b*x)^3)*x,x]
[Out]
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Maple [F] time = 0.02, size = 0, normalized size = 0. \[ \int{f}^{c \left ( bx+a \right ) ^{3}}x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(c*(b*x+a)^3)*x,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int f^{{\left (b x + a\right )}^{3} c} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^((b*x + a)^3*c)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2687, size = 144, normalized size = 1.57 \[ \frac{\left (-b^{3} c \log \left (f\right )\right )^{\frac{1}{3}} a \Gamma \left (\frac{1}{3}, -{\left (b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c\right )} \log \left (f\right )\right ) - b \Gamma \left (\frac{2}{3}, -{\left (b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c\right )} \log \left (f\right )\right )}{3 \, \left (-b^{3} c \log \left (f\right )\right )^{\frac{2}{3}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^((b*x + a)^3*c)*x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{c \left (a + b x\right )^{3}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(c*(b*x+a)**3)*x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{{\left (b x + a\right )}^{3} c} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^((b*x + a)^3*c)*x,x, algorithm="giac")
[Out]