Optimal. Leaf size=34 \[ \frac{x^{1-m} (-a-b x)^{-n} (a+b x)^n}{1-m} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0148539, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ \frac{x^{1-m} (-a-b x)^{-n} (a+b x)^n}{1-m} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^n/(x^m*(-a - b*x)^n),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.50403, size = 22, normalized size = 0.65 \[ \frac{x^{- m + 1} \left (- a - b x\right )^{- n} \left (a + b x\right )^{n}}{- m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**n/(x**m)/((-b*x-a)**n),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.010617, size = 34, normalized size = 1. \[ \frac{x^{1-m} (-a-b x)^{-n} (a+b x)^n}{1-m} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^n/(x^m*(-a - b*x)^n),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 33, normalized size = 1. \[ -{\frac{x \left ( bx+a \right ) ^{n}}{ \left ( -1+m \right ){x}^{m} \left ( -bx-a \right ) ^{n}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^n/(x^m)/((-b*x-a)^n),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.37182, size = 28, normalized size = 0.82 \[ -\frac{x x^{-m}}{\left (-1\right )^{n} m - \left (-1\right )^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n/((-b*x - a)^n*x^m),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.256507, size = 23, normalized size = 0.68 \[ -\frac{x \cos \left (\pi n\right )}{{\left (m - 1\right )} x^{m}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n/((-b*x - a)^n*x^m),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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((b*x+a)**n/(x**m)/((-b*x-a)**n),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.287506, size = 1, normalized size = 0.03 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n/((-b*x - a)^n*x^m),x, algorithm="giac")
[Out]