3.718 \(\int \frac{a+c x^4}{\sqrt{x}} \, dx\)

Optimal. Leaf size=19 \[ 2 a \sqrt{x}+\frac{2}{9} c x^{9/2} \]

[Out]

2*a*Sqrt[x] + (2*c*x^(9/2))/9

_______________________________________________________________________________________

Rubi [A]  time = 0.0137599, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ 2 a \sqrt{x}+\frac{2}{9} c x^{9/2} \]

Antiderivative was successfully verified.

[In]  Int[(a + c*x^4)/Sqrt[x],x]

[Out]

2*a*Sqrt[x] + (2*c*x^(9/2))/9

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.63539, size = 17, normalized size = 0.89 \[ 2 a \sqrt{x} + \frac{2 c x^{\frac{9}{2}}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((c*x**4+a)/x**(1/2),x)

[Out]

2*a*sqrt(x) + 2*c*x**(9/2)/9

_______________________________________________________________________________________

Mathematica [A]  time = 0.00657469, size = 19, normalized size = 1. \[ 2 a \sqrt{x}+\frac{2}{9} c x^{9/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + c*x^4)/Sqrt[x],x]

[Out]

2*a*Sqrt[x] + (2*c*x^(9/2))/9

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 15, normalized size = 0.8 \[{\frac{2\,c{x}^{4}+18\,a}{9}\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+a)/x^(1/2),x)

[Out]

2/9*x^(1/2)*(c*x^4+9*a)

_______________________________________________________________________________________

Maxima [A]  time = 1.43583, size = 18, normalized size = 0.95 \[ \frac{2}{9} \, c x^{\frac{9}{2}} + 2 \, a \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/9*c*x^(9/2) + 2*a*sqrt(x)

_______________________________________________________________________________________

Fricas [A]  time = 0.239344, size = 19, normalized size = 1. \[ \frac{2}{9} \,{\left (c x^{4} + 9 \, a\right )} \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/9*(c*x^4 + 9*a)*sqrt(x)

_______________________________________________________________________________________

Sympy [A]  time = 1.95418, size = 17, normalized size = 0.89 \[ 2 a \sqrt{x} + \frac{2 c x^{\frac{9}{2}}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+a)/x**(1/2),x)

[Out]

2*a*sqrt(x) + 2*c*x**(9/2)/9

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211987, size = 18, normalized size = 0.95 \[ \frac{2}{9} \, c x^{\frac{9}{2}} + 2 \, a \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/9*c*x^(9/2) + 2*a*sqrt(x)