Optimal. Leaf size=14 \[ -\frac{1}{7 d (c+d x)^7} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00701691, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{1}{7 d (c+d x)^7} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^(-8),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.4395, size = 12, normalized size = 0.86 \[ - \frac{1}{7 d \left (c + d x\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(d*x+c)**8,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00436649, size = 14, normalized size = 1. \[ -\frac{1}{7 d (c+d x)^7} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^(-8),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[ -{\frac{1}{7\,d \left ( dx+c \right ) ^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(d*x+c)^8,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.40858, size = 16, normalized size = 1.14 \[ -\frac{1}{7 \,{\left (d x + c\right )}^{7} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-8),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219808, size = 107, normalized size = 7.64 \[ -\frac{1}{7 \,{\left (d^{8} x^{7} + 7 \, c d^{7} x^{6} + 21 \, c^{2} d^{6} x^{5} + 35 \, c^{3} d^{5} x^{4} + 35 \, c^{4} d^{4} x^{3} + 21 \, c^{5} d^{3} x^{2} + 7 \, c^{6} d^{2} x + c^{7} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-8),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.11586, size = 85, normalized size = 6.07 \[ - \frac{1}{7 c^{7} d + 49 c^{6} d^{2} x + 147 c^{5} d^{3} x^{2} + 245 c^{4} d^{4} x^{3} + 245 c^{3} d^{5} x^{4} + 147 c^{2} d^{6} x^{5} + 49 c d^{7} x^{6} + 7 d^{8} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(d*x+c)**8,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220764, size = 16, normalized size = 1.14 \[ -\frac{1}{7 \,{\left (d x + c\right )}^{7} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-8),x, algorithm="giac")
[Out]