Optimal. Leaf size=44 \[ \frac{\left (\frac{b x^2}{2}+\frac{c x^3}{3}\right )^{n+1}}{n+1}+\frac{b x^2}{2}+\frac{c x^3}{3} \]
[Out]
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Rubi [A] time = 0.0206251, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.032 \[ \frac{\left (\frac{b x^2}{2}+\frac{c x^3}{3}\right )^{n+1}}{n+1}+\frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(b*x + c*x^2)*(1 + ((b*x^2)/2 + (c*x^3)/3)^n),x]
[Out]
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Rubi in Sympy [A] time = 3.32383, size = 32, normalized size = 0.73 \[ \frac{b x^{2}}{2} + \frac{c x^{3}}{3} + \frac{\left (\frac{b x^{2}}{2} + \frac{c x^{3}}{3}\right )^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x)*(1+(1/2*b*x**2+1/3*c*x**3)**n),x)
[Out]
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Mathematica [A] time = 0.0371577, size = 42, normalized size = 0.95 \[ \frac{x^2 (3 b+2 c x) \left (\left (\frac{b x^2}{2}+\frac{c x^3}{3}\right )^n+n+1\right )}{6 (n+1)} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x + c*x^2)*(1 + ((b*x^2)/2 + (c*x^3)/3)^n),x]
[Out]
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Maple [A] time = 0.004, size = 37, normalized size = 0.8 \[{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}}+{\frac{1}{1+n} \left ({\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}} \right ) ^{1+n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x)*(1+(1/2*b*x^2+1/3*c*x^3)^n),x)
[Out]
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Maxima [A] time = 0.992911, size = 96, normalized size = 2.18 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + \frac{{\left (2 \, c x^{3} + 3 \, b x^{2}\right )} e^{\left (n \log \left (2 \, c x + 3 \, b\right ) + 2 \, n \log \left (x\right )\right )}}{3^{n + 1} 2^{n + 1} n + 3^{n + 1} 2^{n + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*((1/3*c*x^3 + 1/2*b*x^2)^n + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.279799, size = 77, normalized size = 1.75 \[ \frac{2 \,{\left (c n + c\right )} x^{3} + 3 \,{\left (b n + b\right )} x^{2} +{\left (2 \, c x^{3} + 3 \, b x^{2}\right )}{\left (\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2}\right )}^{n}}{6 \,{\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*((1/3*c*x^3 + 1/2*b*x^2)^n + 1),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x)*(1+(1/2*b*x**2+1/3*c*x**3)**n),x)
[Out]
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GIAC/XCAS [A] time = 0.260366, size = 49, normalized size = 1.11 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + \frac{{\left (\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2}\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*((1/3*c*x^3 + 1/2*b*x^2)^n + 1),x, algorithm="giac")
[Out]