Optimal. Leaf size=64 \[ -\frac{36 d (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)^2}-\frac{6}{\sqrt [6]{a+b x} (c+d x)^{5/6} (b c-a d)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0535162, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{36 d (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)^2}-\frac{6}{\sqrt [6]{a+b x} (c+d x)^{5/6} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(7/6)*(c + d*x)^(11/6)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.79483, size = 54, normalized size = 0.84 \[ - \frac{36 d \left (a + b x\right )^{\frac{5}{6}}}{5 \left (c + d x\right )^{\frac{5}{6}} \left (a d - b c\right )^{2}} + \frac{6}{\sqrt [6]{a + b x} \left (c + d x\right )^{\frac{5}{6}} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(7/6)/(d*x+c)**(11/6),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0686956, size = 45, normalized size = 0.7 \[ -\frac{6 (a d+5 b c+6 b d x)}{5 \sqrt [6]{a+b x} (c+d x)^{5/6} (b c-a d)^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(11/6)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 53, normalized size = 0.8 \[ -{\frac{36\,bdx+6\,ad+30\,bc}{5\,{a}^{2}{d}^{2}-10\,abcd+5\,{b}^{2}{c}^{2}}{\frac{1}{\sqrt [6]{bx+a}}} \left ( dx+c \right ) ^{-{\frac{5}{6}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(7/6)/(d*x+c)^(11/6),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{11}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(11/6)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21362, size = 70, normalized size = 1.09 \[ -\frac{6 \,{\left (6 \, b d x + 5 \, b c + a d\right )}}{5 \,{\left (b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right )}{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{5}{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(11/6)),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(1/(b*x+a)**(7/6)/(d*x+c)**(11/6),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{11}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(11/6)),x, algorithm="giac")
[Out]