Optimal. Leaf size=57 \[ \frac{(d+e x)^4 \left (a e^2+c d^2\right )}{4 e^3}+\frac{c (d+e x)^6}{6 e^3}-\frac{2 c d (d+e x)^5}{5 e^3} \]
[Out]
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Rubi [A] time = 0.116501, antiderivative size = 57, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{(d+e x)^4 \left (a e^2+c d^2\right )}{4 e^3}+\frac{c (d+e x)^6}{6 e^3}-\frac{2 c d (d+e x)^5}{5 e^3} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^3*(a + c*x^2),x]
[Out]
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Rubi in Sympy [A] time = 15.4967, size = 51, normalized size = 0.89 \[ - \frac{2 c d \left (d + e x\right )^{5}}{5 e^{3}} + \frac{c \left (d + e x\right )^{6}}{6 e^{3}} + \frac{\left (d + e x\right )^{4} \left (a e^{2} + c d^{2}\right )}{4 e^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**3*(c*x**2+a),x)
[Out]
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Mathematica [A] time = 0.0245485, size = 74, normalized size = 1.3 \[ \frac{1}{4} a x \left (4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right )+\frac{1}{60} c x^3 \left (20 d^3+45 d^2 e x+36 d e^2 x^2+10 e^3 x^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^3*(a + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 73, normalized size = 1.3 \[{\frac{{e}^{3}c{x}^{6}}{6}}+{\frac{3\,d{e}^{2}c{x}^{5}}{5}}+{\frac{ \left ({e}^{3}a+3\,{d}^{2}ec \right ){x}^{4}}{4}}+{\frac{ \left ( 3\,d{e}^{2}a+{d}^{3}c \right ){x}^{3}}{3}}+{\frac{3\,{d}^{2}ea{x}^{2}}{2}}+{d}^{3}ax \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^3*(c*x^2+a),x)
[Out]
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Maxima [A] time = 0.721717, size = 97, normalized size = 1.7 \[ \frac{1}{6} \, c e^{3} x^{6} + \frac{3}{5} \, c d e^{2} x^{5} + \frac{3}{2} \, a d^{2} e x^{2} + a d^{3} x + \frac{1}{4} \,{\left (3 \, c d^{2} e + a e^{3}\right )} x^{4} + \frac{1}{3} \,{\left (c d^{3} + 3 \, a d e^{2}\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(e*x + d)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198428, size = 1, normalized size = 0.02 \[ \frac{1}{6} x^{6} e^{3} c + \frac{3}{5} x^{5} e^{2} d c + \frac{3}{4} x^{4} e d^{2} c + \frac{1}{4} x^{4} e^{3} a + \frac{1}{3} x^{3} d^{3} c + x^{3} e^{2} d a + \frac{3}{2} x^{2} e d^{2} a + x d^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(e*x + d)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.119669, size = 80, normalized size = 1.4 \[ a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + \frac{3 c d e^{2} x^{5}}{5} + \frac{c e^{3} x^{6}}{6} + x^{4} \left (\frac{a e^{3}}{4} + \frac{3 c d^{2} e}{4}\right ) + x^{3} \left (a d e^{2} + \frac{c d^{3}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**3*(c*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.205048, size = 96, normalized size = 1.68 \[ \frac{1}{6} \, c x^{6} e^{3} + \frac{3}{5} \, c d x^{5} e^{2} + \frac{3}{4} \, c d^{2} x^{4} e + \frac{1}{3} \, c d^{3} x^{3} + \frac{1}{4} \, a x^{4} e^{3} + a d x^{3} e^{2} + \frac{3}{2} \, a d^{2} x^{2} e + a d^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(e*x + d)^3,x, algorithm="giac")
[Out]