Optimal. Leaf size=34 \[ \frac{\left (c d^2+2 c d e x+c e^2 x^2\right )^{7/2}}{7 c e} \]
[Out]
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Rubi [A] time = 0.0210837, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.033 \[ \frac{\left (c d^2+2 c d e x+c e^2 x^2\right )^{7/2}}{7 c e} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 9.3353, size = 29, normalized size = 0.85 \[ \frac{\left (c d^{2} + 2 c d e x + c e^{2} x^{2}\right )^{\frac{7}{2}}}{7 c e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0394721, size = 23, normalized size = 0.68 \[ \frac{\left (c (d+e x)^2\right )^{7/2}}{7 c e} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]
[Out]
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Maple [B] time = 0.005, size = 95, normalized size = 2.8 \[{\frac{x \left ({e}^{6}{x}^{6}+7\,d{e}^{5}{x}^{5}+21\,{d}^{2}{e}^{4}{x}^{4}+35\,{d}^{3}{e}^{3}{x}^{3}+35\,{d}^{4}{e}^{2}{x}^{2}+21\,{d}^{5}ex+7\,{d}^{6} \right ) }{7\, \left ( ex+d \right ) ^{5}} \left ( c{e}^{2}{x}^{2}+2\,cdex+c{d}^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)
[Out]
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Maxima [A] time = 0.678636, size = 41, normalized size = 1.21 \[ \frac{{\left (c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right )}^{\frac{7}{2}}}{7 \, c e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(5/2)*(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214473, size = 158, normalized size = 4.65 \[ \frac{{\left (c^{2} e^{6} x^{7} + 7 \, c^{2} d e^{5} x^{6} + 21 \, c^{2} d^{2} e^{4} x^{5} + 35 \, c^{2} d^{3} e^{3} x^{4} + 35 \, c^{2} d^{4} e^{2} x^{3} + 21 \, c^{2} d^{5} e x^{2} + 7 \, c^{2} d^{6} x\right )} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{7 \,{\left (e x + d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(5/2)*(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 21.3949, size = 287, normalized size = 8.44 \[ \begin{cases} \frac{c^{2} d^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7 e} + \frac{6 c^{2} d^{5} x \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{15 c^{2} d^{4} e x^{2} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{20 c^{2} d^{3} e^{2} x^{3} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{15 c^{2} d^{2} e^{3} x^{4} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{6 c^{2} d e^{4} x^{5} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} + \frac{c^{2} e^{5} x^{6} \sqrt{c d^{2} + 2 c d e x + c e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\d x \left (c d^{2}\right )^{\frac{5}{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.222139, size = 138, normalized size = 4.06 \[ \frac{1}{7} \,{\left (c^{2} d^{6} e^{\left (-1\right )} +{\left (6 \, c^{2} d^{5} +{\left (15 \, c^{2} d^{4} e +{\left (20 \, c^{2} d^{3} e^{2} +{\left (15 \, c^{2} d^{2} e^{3} +{\left (c^{2} x e^{5} + 6 \, c^{2} d e^{4}\right )} x\right )} x\right )} x\right )} x\right )} x\right )} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(5/2)*(e*x + d),x, algorithm="giac")
[Out]