Optimal. Leaf size=38 \[ a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {194} \[ \frac {3}{5} a^2 b x^5+a^3 x+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 194
Rubi steps
\begin {align*} \int \left (a+b x^4\right )^3 \, dx &=\int \left (a^3+3 a^2 b x^4+3 a b^2 x^8+b^3 x^{12}\right ) \, dx\\ &=a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 38, normalized size = 1.00 \[ a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 32, normalized size = 0.84 \[ \frac {1}{13} x^{13} b^{3} + \frac {1}{3} x^{9} b^{2} a + \frac {3}{5} x^{5} b a^{2} + x a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 32, normalized size = 0.84 \[ \frac {1}{13} \, b^{3} x^{13} + \frac {1}{3} \, a b^{2} x^{9} + \frac {3}{5} \, a^{2} b x^{5} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 33, normalized size = 0.87 \[ \frac {1}{13} b^{3} x^{13}+\frac {1}{3} a \,b^{2} x^{9}+\frac {3}{5} a^{2} b \,x^{5}+a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.35, size = 32, normalized size = 0.84 \[ \frac {1}{13} \, b^{3} x^{13} + \frac {1}{3} \, a b^{2} x^{9} + \frac {3}{5} \, a^{2} b x^{5} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 32, normalized size = 0.84 \[ a^3\,x+\frac {3\,a^2\,b\,x^5}{5}+\frac {a\,b^2\,x^9}{3}+\frac {b^3\,x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 34, normalized size = 0.89 \[ a^{3} x + \frac {3 a^{2} b x^{5}}{5} + \frac {a b^{2} x^{9}}{3} + \frac {b^{3} x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________