Optimal. Leaf size=34 \[ \frac{b (c x)^{m+3}}{c^3 (m+3)}+\frac{(c x)^{m+5}}{c^4 (m+5)} \]
[Out]
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Rubi [A] time = 0.0361338, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{b (c x)^{m+3}}{c^3 (m+3)}+\frac{(c x)^{m+5}}{c^4 (m+5)} \]
Antiderivative was successfully verified.
[In] Int[(c*x)^m*(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [A] time = 10.1091, size = 27, normalized size = 0.79 \[ \frac{b \left (c x\right )^{m + 3}}{c^{3} \left (m + 3\right )} + \frac{\left (c x\right )^{m + 5}}{c^{4} \left (m + 5\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x)**m*(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.0275057, size = 27, normalized size = 0.79 \[ (c x)^m \left (\frac{b x^3}{m+3}+\frac{c x^5}{m+5}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(c*x)^m*(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.003, size = 39, normalized size = 1.2 \[{\frac{ \left ( cx \right ) ^{m} \left ( cm{x}^{2}+3\,c{x}^{2}+bm+5\,b \right ){x}^{3}}{ \left ( 5+m \right ) \left ( 3+m \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x)^m*(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 0.69625, size = 46, normalized size = 1.35 \[ \frac{c^{m + 1} x^{5} x^{m}}{m + 5} + \frac{b c^{m} x^{3} x^{m}}{m + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(c*x)^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271867, size = 53, normalized size = 1.56 \[ \frac{{\left ({\left (c m + 3 \, c\right )} x^{5} +{\left (b m + 5 \, b\right )} x^{3}\right )} \left (c x\right )^{m}}{m^{2} + 8 \, m + 15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(c*x)^m,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.9643, size = 119, normalized size = 3.5 \[ \begin{cases} \frac{- \frac{b}{2 x^{2}} + c \log{\left (x \right )}}{c^{5}} & \text{for}\: m = -5 \\\frac{b \log{\left (x \right )} + \frac{c x^{2}}{2}}{c^{3}} & \text{for}\: m = -3 \\\frac{b c^{m} m x^{3} x^{m}}{m^{2} + 8 m + 15} + \frac{5 b c^{m} x^{3} x^{m}}{m^{2} + 8 m + 15} + \frac{c c^{m} m x^{5} x^{m}}{m^{2} + 8 m + 15} + \frac{3 c c^{m} x^{5} x^{m}}{m^{2} + 8 m + 15} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)**m*(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.271009, size = 86, normalized size = 2.53 \[ \frac{c m x^{5} e^{\left (m{\rm ln}\left (c x\right )\right )} + 3 \, c x^{5} e^{\left (m{\rm ln}\left (c x\right )\right )} + b m x^{3} e^{\left (m{\rm ln}\left (c x\right )\right )} + 5 \, b x^{3} e^{\left (m{\rm ln}\left (c x\right )\right )}}{m^{2} + 8 \, m + 15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(c*x)^m,x, algorithm="giac")
[Out]