Optimal. Leaf size=17 \[ \frac{(a+b x)^4}{4 b c^2} \]
[Out]
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Rubi [A] time = 0.0116, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{(a+b x)^4}{4 b c^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/(a*c + b*c*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 4.35229, size = 12, normalized size = 0.71 \[ \frac{\left (a + b x\right )^{4}}{4 b c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/(b*c*x+a*c)**2,x)
[Out]
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Mathematica [A] time = 0.00229364, size = 17, normalized size = 1. \[ \frac{(a+b x)^4}{4 b c^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/(a*c + b*c*x)^2,x]
[Out]
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \[{\frac{ \left ( bx+a \right ) ^{4}}{4\,b{c}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/(b*c*x+a*c)^2,x)
[Out]
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Maxima [A] time = 1.33756, size = 50, normalized size = 2.94 \[ \frac{b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a^{3} x}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.188796, size = 50, normalized size = 2.94 \[ \frac{b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a^{3} x}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.204478, size = 46, normalized size = 2.71 \[ \frac{a^{3} x}{c^{2}} + \frac{3 a^{2} b x^{2}}{2 c^{2}} + \frac{a b^{2} x^{3}}{c^{2}} + \frac{b^{3} x^{4}}{4 c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/(b*c*x+a*c)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.205819, size = 24, normalized size = 1.41 \[ \frac{{\left (b c x + a c\right )}^{4}}{4 \, b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^2,x, algorithm="giac")
[Out]