3.1279 \(\int \frac{x^4}{\left (a+b x^5\right )^2} \, dx\)

Optimal. Leaf size=16 \[ -\frac{1}{5 b \left (a+b x^5\right )} \]

[Out]

-1/(5*b*(a + b*x^5))

_______________________________________________________________________________________

Rubi [A]  time = 0.00987596, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{5 b \left (a+b x^5\right )} \]

Antiderivative was successfully verified.

[In]  Int[x^4/(a + b*x^5)^2,x]

[Out]

-1/(5*b*(a + b*x^5))

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.11381, size = 12, normalized size = 0.75 \[ - \frac{1}{5 b \left (a + b x^{5}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4/(b*x**5+a)**2,x)

[Out]

-1/(5*b*(a + b*x**5))

_______________________________________________________________________________________

Mathematica [A]  time = 0.00786806, size = 16, normalized size = 1. \[ -\frac{1}{5 b \left (a+b x^5\right )} \]

Antiderivative was successfully verified.

[In]  Integrate[x^4/(a + b*x^5)^2,x]

[Out]

-1/(5*b*(a + b*x^5))

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{5\,b \left ( b{x}^{5}+a \right ) }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4/(b*x^5+a)^2,x)

[Out]

-1/5/b/(b*x^5+a)

_______________________________________________________________________________________

Maxima [A]  time = 1.43769, size = 19, normalized size = 1.19 \[ -\frac{1}{5 \,{\left (b x^{5} + a\right )} b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(b*x^5 + a)^2,x, algorithm="maxima")

[Out]

-1/5/((b*x^5 + a)*b)

_______________________________________________________________________________________

Fricas [A]  time = 0.219039, size = 20, normalized size = 1.25 \[ -\frac{1}{5 \,{\left (b^{2} x^{5} + a b\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(b*x^5 + a)^2,x, algorithm="fricas")

[Out]

-1/5/(b^2*x^5 + a*b)

_______________________________________________________________________________________

Sympy [A]  time = 2.19796, size = 15, normalized size = 0.94 \[ - \frac{1}{5 a b + 5 b^{2} x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4/(b*x**5+a)**2,x)

[Out]

-1/(5*a*b + 5*b**2*x**5)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.227402, size = 19, normalized size = 1.19 \[ -\frac{1}{5 \,{\left (b x^{5} + a\right )} b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(b*x^5 + a)^2,x, algorithm="giac")

[Out]

-1/5/((b*x^5 + a)*b)