Optimal. Leaf size=30 \[ \frac{1}{6} \left (a x+\frac{c x^3}{3}\right )^6+a x+\frac{c x^3}{3} \]
[Out]
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Rubi [A] time = 0.0295571, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{\left (3 a x+c x^3\right )^6}{4374}+a x+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^2)*(1 + (a*x + (c*x^3)/3)^5),x]
[Out]
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Rubi in Sympy [A] time = 4.07227, size = 22, normalized size = 0.73 \[ a x + \frac{c x^{3}}{3} + \frac{\left (a x + \frac{c x^{3}}{3}\right )^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+a)*(1+(a*x+1/3*c*x**3)**5),x)
[Out]
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Mathematica [B] time = 0.00919983, size = 93, normalized size = 3.1 \[ \frac{a^6 x^6}{6}+\frac{1}{3} a^5 c x^8+\frac{5}{18} a^4 c^2 x^{10}+\frac{10}{81} a^3 c^3 x^{12}+\frac{5}{162} a^2 c^4 x^{14}+\frac{1}{243} a c^5 x^{16}+a x+\frac{c^6 x^{18}}{4374}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^2)*(1 + (a*x + (c*x^3)/3)^5),x]
[Out]
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Maple [B] time = 0.005, size = 78, normalized size = 2.6 \[{\frac{{c}^{6}{x}^{18}}{4374}}+{\frac{a{c}^{5}{x}^{16}}{243}}+{\frac{5\,{a}^{2}{c}^{4}{x}^{14}}{162}}+{\frac{10\,{a}^{3}{c}^{3}{x}^{12}}{81}}+{\frac{5\,{a}^{4}{c}^{2}{x}^{10}}{18}}+{\frac{{a}^{5}c{x}^{8}}{3}}+{\frac{{a}^{6}{x}^{6}}{6}}+{\frac{c{x}^{3}}{3}}+ax \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+a)*(1+(a*x+1/3*c*x^3)^5),x)
[Out]
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Maxima [A] time = 0.80384, size = 104, normalized size = 3.47 \[ \frac{1}{4374} \, c^{6} x^{18} + \frac{1}{243} \, a c^{5} x^{16} + \frac{5}{162} \, a^{2} c^{4} x^{14} + \frac{10}{81} \, a^{3} c^{3} x^{12} + \frac{5}{18} \, a^{4} c^{2} x^{10} + \frac{1}{3} \, a^{5} c x^{8} + \frac{1}{6} \, a^{6} x^{6} + \frac{1}{3} \, c x^{3} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/243*((c*x^3 + 3*a*x)^5 + 243)*(c*x^2 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256895, size = 104, normalized size = 3.47 \[ \frac{1}{4374} \, c^{6} x^{18} + \frac{1}{243} \, a c^{5} x^{16} + \frac{5}{162} \, a^{2} c^{4} x^{14} + \frac{10}{81} \, a^{3} c^{3} x^{12} + \frac{5}{18} \, a^{4} c^{2} x^{10} + \frac{1}{3} \, a^{5} c x^{8} + \frac{1}{6} \, a^{6} x^{6} + \frac{1}{3} \, c x^{3} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/243*((c*x^3 + 3*a*x)^5 + 243)*(c*x^2 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.174432, size = 87, normalized size = 2.9 \[ \frac{a^{6} x^{6}}{6} + \frac{a^{5} c x^{8}}{3} + \frac{5 a^{4} c^{2} x^{10}}{18} + \frac{10 a^{3} c^{3} x^{12}}{81} + \frac{5 a^{2} c^{4} x^{14}}{162} + \frac{a c^{5} x^{16}}{243} + a x + \frac{c^{6} x^{18}}{4374} + \frac{c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+a)*(1+(a*x+1/3*c*x**3)**5),x)
[Out]
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GIAC/XCAS [A] time = 0.258867, size = 104, normalized size = 3.47 \[ \frac{1}{4374} \, c^{6} x^{18} + \frac{1}{243} \, a c^{5} x^{16} + \frac{5}{162} \, a^{2} c^{4} x^{14} + \frac{10}{81} \, a^{3} c^{3} x^{12} + \frac{5}{18} \, a^{4} c^{2} x^{10} + \frac{1}{3} \, a^{5} c x^{8} + \frac{1}{6} \, a^{6} x^{6} + \frac{1}{3} \, c x^{3} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/243*((c*x^3 + 3*a*x)^5 + 243)*(c*x^2 + a),x, algorithm="giac")
[Out]