Optimal. Leaf size=18 \[ \frac{\left (a+b x^4\right )^{7/4}}{7 b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0102302, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a+b x^4\right )^{7/4}}{7 b} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.1277, size = 12, normalized size = 0.67 \[ \frac{\left (a + b x^{4}\right )^{\frac{7}{4}}}{7 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00852947, size = 18, normalized size = 1. \[ \frac{\left (a+b x^4\right )^{7/4}}{7 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 15, normalized size = 0.8 \[{\frac{1}{7\,b} \left ( b{x}^{4}+a \right ) ^{{\frac{7}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^4+a)^(3/4),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41847, size = 19, normalized size = 1.06 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)*x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.324294, size = 19, normalized size = 1.06 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)*x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.86567, size = 39, normalized size = 2.17 \[ \begin{cases} \frac{a \left (a + b x^{4}\right )^{\frac{3}{4}}}{7 b} + \frac{x^{4} \left (a + b x^{4}\right )^{\frac{3}{4}}}{7} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{4}} x^{4}}{4} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215634, size = 19, normalized size = 1.06 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)*x^3,x, algorithm="giac")
[Out]