3.611 \(\int \frac{a+b x^4}{x^4} \, dx\)

Optimal. Leaf size=12 \[ b x-\frac{a}{3 x^3} \]

[Out]

-a/(3*x^3) + b*x

_______________________________________________________________________________________

Rubi [A]  time = 0.012304, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ b x-\frac{a}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^4,x]

[Out]

-a/(3*x^3) + b*x

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{a}{3 x^{3}} + \int b\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/(3*x**3) + Integral(b, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00165271, size = 12, normalized size = 1. \[ b x-\frac{a}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^4,x]

[Out]

-a/(3*x^3) + b*x

_______________________________________________________________________________________

Maple [A]  time = 0.006, size = 11, normalized size = 0.9 \[ -{\frac{a}{3\,{x}^{3}}}+bx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^4,x)

[Out]

-1/3*a/x^3+b*x

_______________________________________________________________________________________

Maxima [A]  time = 1.44679, size = 14, normalized size = 1.17 \[ b x - \frac{a}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x - 1/3*a/x^3

_______________________________________________________________________________________

Fricas [A]  time = 0.226431, size = 20, normalized size = 1.67 \[ \frac{3 \, b x^{4} - a}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*(3*b*x^4 - a)/x^3

_______________________________________________________________________________________

Sympy [A]  time = 1.01382, size = 8, normalized size = 0.67 \[ - \frac{a}{3 x^{3}} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**4,x)

[Out]

-a/(3*x**3) + b*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.222555, size = 14, normalized size = 1.17 \[ b x - \frac{a}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x - 1/3*a/x^3