Optimal. Leaf size=135 \[ \frac{\left (d^3+e^3 x^3\right )^p \left (1+\frac{2 (d+e x)}{\left (-3+i \sqrt{3}\right ) d}\right )^{-p} \left (1-\frac{2 (d+e x)}{\left (3+i \sqrt{3}\right ) d}\right )^{-p} F_1\left (p;-p,-p;p+1;-\frac{2 (d+e x)}{\left (-3+i \sqrt{3}\right ) d},\frac{2 (d+e x)}{\left (3+i \sqrt{3}\right ) d}\right )}{e p} \]
[Out]
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Rubi [F] time = 0.121845, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{\left (d^3+e^3 x^3\right )^p}{d+e x},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(d^3 + e^3*x^3)^p/(d + e*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (d^{3} + e^{3} x^{3}\right )^{p}}{d + e x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e**3*x**3+d**3)**p/(e*x+d),x)
[Out]
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Mathematica [A] time = 0.0431622, size = 0, normalized size = 0. \[ \int \frac{\left (d^3+e^3 x^3\right )^p}{d+e x} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(d^3 + e^3*x^3)^p/(d + e*x),x]
[Out]
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Maple [F] time = 0.087, size = 0, normalized size = 0. \[ \int{\frac{ \left ({e}^{3}{x}^{3}+{d}^{3} \right ) ^{p}}{ex+d}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e^3*x^3+d^3)^p/(e*x+d),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (e^{3} x^{3} + d^{3}\right )}^{p}}{e x + d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^3*x^3 + d^3)^p/(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (e^{3} x^{3} + d^{3}\right )}^{p}}{e x + d}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^3*x^3 + d^3)^p/(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 164.096, size = 638, normalized size = 4.73 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e**3*x**3+d**3)**p/(e*x+d),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (e^{3} x^{3} + d^{3}\right )}^{p}}{e x + d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^3*x^3 + d^3)^p/(e*x + d),x, algorithm="giac")
[Out]