3.1809 \(\int \frac{1}{\sqrt [6]{a+b x} (c+d x)^{11/6}} \, dx\)

Optimal. Leaf size=32 \[ \frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)} \]

[Out]

(6*(a + b*x)^(5/6))/(5*(b*c - a*d)*(c + d*x)^(5/6))

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Rubi [A]  time = 0.0225633, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)} \]

Antiderivative was successfully verified.

[In]  Int[1/((a + b*x)^(1/6)*(c + d*x)^(11/6)),x]

[Out]

(6*(a + b*x)^(5/6))/(5*(b*c - a*d)*(c + d*x)^(5/6))

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Rubi in Sympy [A]  time = 3.40151, size = 27, normalized size = 0.84 \[ - \frac{6 \left (a + b x\right )^{\frac{5}{6}}}{5 \left (c + d x\right )^{\frac{5}{6}} \left (a d - b c\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(b*x+a)**(1/6)/(d*x+c)**(11/6),x)

[Out]

-6*(a + b*x)**(5/6)/(5*(c + d*x)**(5/6)*(a*d - b*c))

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Mathematica [A]  time = 0.0446239, size = 32, normalized size = 1. \[ -\frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (a d-b c)} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((a + b*x)^(1/6)*(c + d*x)^(11/6)),x]

[Out]

(-6*(a + b*x)^(5/6))/(5*(-(b*c) + a*d)*(c + d*x)^(5/6))

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Maple [A]  time = 0.005, size = 27, normalized size = 0.8 \[ -{\frac{6}{5\,ad-5\,bc} \left ( bx+a \right ) ^{{\frac{5}{6}}} \left ( dx+c \right ) ^{-{\frac{5}{6}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x+a)^(1/6)/(d*x+c)^(11/6),x)

[Out]

-6/5*(b*x+a)^(5/6)/(d*x+c)^(5/6)/(a*d-b*c)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{11}{6}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((b*x + a)^(1/6)*(d*x + c)^(11/6)),x, algorithm="maxima")

[Out]

integrate(1/((b*x + a)^(1/6)*(d*x + c)^(11/6)), x)

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Fricas [A]  time = 0.222877, size = 35, normalized size = 1.09 \[ \frac{6 \,{\left (b x + a\right )}^{\frac{5}{6}}}{5 \,{\left (b c - a d\right )}{\left (d x + c\right )}^{\frac{5}{6}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((b*x + a)^(1/6)*(d*x + c)^(11/6)),x, algorithm="fricas")

[Out]

6/5*(b*x + a)^(5/6)/((b*c - a*d)*(d*x + c)^(5/6))

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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(1/(b*x+a)**(1/6)/(d*x+c)**(11/6),x)

[Out]

Timed out

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{11}{6}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((b*x + a)^(1/6)*(d*x + c)^(11/6)),x, algorithm="giac")

[Out]

integrate(1/((b*x + a)^(1/6)*(d*x + c)^(11/6)), x)