Optimal. Leaf size=38 \[ \frac{2 a}{3 b c^4 (a-b x)^3}-\frac{1}{2 b c^4 (a-b x)^2} \]
[Out]
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Rubi [A] time = 0.0450027, antiderivative size = 38, 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 \[ \frac{2 a}{3 b c^4 (a-b x)^3}-\frac{1}{2 b c^4 (a-b x)^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/(a*c - b*c*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 10.9593, size = 31, normalized size = 0.82 \[ \frac{2 a}{3 b c^{4} \left (a - b x\right )^{3}} - \frac{1}{2 b c^{4} \left (a - b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/(-b*c*x+a*c)**4,x)
[Out]
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Mathematica [A] time = 0.015675, size = 25, normalized size = 0.66 \[ -\frac{a+3 b x}{6 b c^4 (b x-a)^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/(a*c - b*c*x)^4,x]
[Out]
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Maple [A] time = 0.009, size = 35, normalized size = 0.9 \[{\frac{1}{{c}^{4}} \left ( -{\frac{2\,a}{3\,b \left ( bx-a \right ) ^{3}}}-{\frac{1}{2\,b \left ( bx-a \right ) ^{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/(-b*c*x+a*c)^4,x)
[Out]
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Maxima [A] time = 1.34382, size = 73, normalized size = 1.92 \[ -\frac{3 \, b x + a}{6 \,{\left (b^{4} c^{4} x^{3} - 3 \, a b^{3} c^{4} x^{2} + 3 \, a^{2} b^{2} c^{4} x - a^{3} b c^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(b*c*x - a*c)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212076, size = 73, normalized size = 1.92 \[ -\frac{3 \, b x + a}{6 \,{\left (b^{4} c^{4} x^{3} - 3 \, a b^{3} c^{4} x^{2} + 3 \, a^{2} b^{2} c^{4} x - a^{3} b c^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(b*c*x - a*c)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.74569, size = 56, normalized size = 1.47 \[ - \frac{a + 3 b x}{- 6 a^{3} b c^{4} + 18 a^{2} b^{2} c^{4} x - 18 a b^{3} c^{4} x^{2} + 6 b^{4} c^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/(-b*c*x+a*c)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.203073, size = 31, normalized size = 0.82 \[ -\frac{3 \, b x + a}{6 \,{\left (b x - a\right )}^{3} b c^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/(b*c*x - a*c)^4,x, algorithm="giac")
[Out]