Optimal. Leaf size=64 \[ \frac{b x^{n-1} (a+b x)^{1-n}}{a^2 (1-n) (2-n)}-\frac{x^{n-2} (a+b x)^{1-n}}{a (2-n)} \]
[Out]
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Rubi [A] time = 0.0382108, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{b x^{n-1} (a+b x)^{1-n}}{a^2 (1-n) (2-n)}-\frac{x^{n-2} (a+b x)^{1-n}}{a (2-n)} \]
Antiderivative was successfully verified.
[In] Int[x^(-3 + n)/(a + b*x)^n,x]
[Out]
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Rubi in Sympy [A] time = 7.21266, size = 42, normalized size = 0.66 \[ - \frac{x^{n - 2} \left (a + b x\right )^{- n + 1}}{a \left (- n + 2\right )} + \frac{b x^{n - 1} \left (a + b x\right )^{- n + 1}}{a^{2} \left (- n + 1\right ) \left (- n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-3+n)/((b*x+a)**n),x)
[Out]
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Mathematica [A] time = 0.0470845, size = 39, normalized size = 0.61 \[ \frac{x^{n-2} (a+b x)^{1-n} (a (n-1)+b x)}{a^2 (n-2) (n-1)} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-3 + n)/(a + b*x)^n,x]
[Out]
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Maple [A] time = 0.006, size = 44, normalized size = 0.7 \[{\frac{{x}^{-2+n} \left ( an+bx-a \right ) \left ( bx+a \right ) }{ \left ( bx+a \right ) ^{n} \left ( -2+n \right ) \left ( -1+n \right ){a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-3+n)/((b*x+a)^n),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x + a\right )}^{-n} x^{n - 3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(n - 3)/(b*x + a)^n,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222416, size = 86, normalized size = 1.34 \[ \frac{{\left (a b n x^{2} + b^{2} x^{3} +{\left (a^{2} n - a^{2}\right )} x\right )} x^{n - 3}}{{\left (a^{2} n^{2} - 3 \, a^{2} n + 2 \, a^{2}\right )}{\left (b x + a\right )}^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(n - 3)/(b*x + a)^n,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-3+n)/((b*x+a)**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{n - 3}}{{\left (b x + a\right )}^{n}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(n - 3)/(b*x + a)^n,x, algorithm="giac")
[Out]