Optimal. Leaf size=30 \[ \frac{a}{3 b^2 (a+b x)^3}-\frac{1}{2 b^2 (a+b x)^2} \]
[Out]
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Rubi [A] time = 0.0303053, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a}{3 b^2 (a+b x)^3}-\frac{1}{2 b^2 (a+b x)^2} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 5.5859, size = 26, normalized size = 0.87 \[ \frac{a}{3 b^{2} \left (a + b x\right )^{3}} - \frac{1}{2 b^{2} \left (a + b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x+a)**4,x)
[Out]
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Mathematica [A] time = 0.00747, size = 20, normalized size = 0.67 \[ -\frac{a+3 b x}{6 b^2 (a+b x)^3} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x)^4,x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.9 \[{\frac{a}{3\,{b}^{2} \left ( bx+a \right ) ^{3}}}-{\frac{1}{2\,{b}^{2} \left ( bx+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x+a)^4,x)
[Out]
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Maxima [A] time = 1.3368, size = 58, normalized size = 1.93 \[ -\frac{3 \, b x + a}{6 \,{\left (b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205653, size = 58, normalized size = 1.93 \[ -\frac{3 \, b x + a}{6 \,{\left (b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.49142, size = 44, normalized size = 1.47 \[ - \frac{a + 3 b x}{6 a^{3} b^{2} + 18 a^{2} b^{3} x + 18 a b^{4} x^{2} + 6 b^{5} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x+a)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.200993, size = 24, normalized size = 0.8 \[ -\frac{3 \, b x + a}{6 \,{\left (b x + a\right )}^{3} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^4,x, algorithm="giac")
[Out]