Optimal. Leaf size=19 \[ \frac{\left (b x+c x^2\right )^{p+1}}{p+1} \]
[Out]
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Rubi [A] time = 0.0102823, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{\left (b x+c x^2\right )^{p+1}}{p+1} \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x)*(b*x + c*x^2)^p,x]
[Out]
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Rubi in Sympy [A] time = 3.51661, size = 14, normalized size = 0.74 \[ \frac{\left (b x + c x^{2}\right )^{p + 1}}{p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x+b)*(c*x**2+b*x)**p,x)
[Out]
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Mathematica [A] time = 0.03231, size = 17, normalized size = 0.89 \[ \frac{(x (b+c x))^{p+1}}{p+1} \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x)*(b*x + c*x^2)^p,x]
[Out]
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Maple [A] time = 0.006, size = 24, normalized size = 1.3 \[{\frac{x \left ( cx+b \right ) \left ( c{x}^{2}+bx \right ) ^{p}}{1+p}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x+b)*(c*x^2+b*x)^p,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*(c*x^2 + b*x)^p,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.298969, size = 35, normalized size = 1.84 \[ \frac{{\left (c x^{2} + b x\right )}{\left (c x^{2} + b x\right )}^{p}}{p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*(c*x^2 + b*x)^p,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.72258, size = 46, normalized size = 2.42 \[ \begin{cases} \frac{b x \left (b x + c x^{2}\right )^{p}}{p + 1} + \frac{c x^{2} \left (b x + c x^{2}\right )^{p}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left (x \right )} + \log{\left (\frac{b}{c} + x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x+b)*(c*x**2+b*x)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.264448, size = 55, normalized size = 2.89 \[ \frac{c x^{2} e^{\left (p{\rm ln}\left (c x^{2} + b x\right )\right )} + b x e^{\left (p{\rm ln}\left (c x^{2} + b x\right )\right )}}{p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*(c*x^2 + b*x)^p,x, algorithm="giac")
[Out]