Optimal. Leaf size=66 \[ \frac {a^5 x^2}{2}+a^4 b x^5+\frac {5}{4} a^3 b^2 x^8+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{14} a b^4 x^{14}+\frac {b^5 x^{17}}{17} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {270} \[ \frac {10}{11} a^2 b^3 x^{11}+\frac {5}{4} a^3 b^2 x^8+a^4 b x^5+\frac {a^5 x^2}{2}+\frac {5}{14} a b^4 x^{14}+\frac {b^5 x^{17}}{17} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rubi steps
\begin {align*} \int x \left (a+b x^3\right )^5 \, dx &=\int \left (a^5 x+5 a^4 b x^4+10 a^3 b^2 x^7+10 a^2 b^3 x^{10}+5 a b^4 x^{13}+b^5 x^{16}\right ) \, dx\\ &=\frac {a^5 x^2}{2}+a^4 b x^5+\frac {5}{4} a^3 b^2 x^8+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{14} a b^4 x^{14}+\frac {b^5 x^{17}}{17}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 66, normalized size = 1.00 \[ \frac {a^5 x^2}{2}+a^4 b x^5+\frac {5}{4} a^3 b^2 x^8+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{14} a b^4 x^{14}+\frac {b^5 x^{17}}{17} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.56, size = 56, normalized size = 0.85 \[ \frac {1}{17} x^{17} b^{5} + \frac {5}{14} x^{14} b^{4} a + \frac {10}{11} x^{11} b^{3} a^{2} + \frac {5}{4} x^{8} b^{2} a^{3} + x^{5} b a^{4} + \frac {1}{2} x^{2} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 56, normalized size = 0.85 \[ \frac {1}{17} \, b^{5} x^{17} + \frac {5}{14} \, a b^{4} x^{14} + \frac {10}{11} \, a^{2} b^{3} x^{11} + \frac {5}{4} \, a^{3} b^{2} x^{8} + a^{4} b x^{5} + \frac {1}{2} \, a^{5} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 57, normalized size = 0.86 \[ \frac {1}{17} b^{5} x^{17}+\frac {5}{14} a \,b^{4} x^{14}+\frac {10}{11} a^{2} b^{3} x^{11}+\frac {5}{4} a^{3} b^{2} x^{8}+a^{4} b \,x^{5}+\frac {1}{2} a^{5} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 56, normalized size = 0.85 \[ \frac {1}{17} \, b^{5} x^{17} + \frac {5}{14} \, a b^{4} x^{14} + \frac {10}{11} \, a^{2} b^{3} x^{11} + \frac {5}{4} \, a^{3} b^{2} x^{8} + a^{4} b x^{5} + \frac {1}{2} \, a^{5} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 56, normalized size = 0.85 \[ \frac {a^5\,x^2}{2}+a^4\,b\,x^5+\frac {5\,a^3\,b^2\,x^8}{4}+\frac {10\,a^2\,b^3\,x^{11}}{11}+\frac {5\,a\,b^4\,x^{14}}{14}+\frac {b^5\,x^{17}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 63, normalized size = 0.95 \[ \frac {a^{5} x^{2}}{2} + a^{4} b x^{5} + \frac {5 a^{3} b^{2} x^{8}}{4} + \frac {10 a^{2} b^{3} x^{11}}{11} + \frac {5 a b^{4} x^{14}}{14} + \frac {b^{5} x^{17}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________