Optimal. Leaf size=16 \[ \frac {\left (a+b x^{25}\right )^{13}}{325 b} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \begin {gather*} \frac {\left (a+b x^{25}\right )^{13}}{325 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin {align*} \int x^{24} \left (a+b x^{25}\right )^{12} \, dx &=\frac {\left (a+b x^{25}\right )^{13}}{325 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.01, size = 160, normalized size = 10.00 \begin {gather*} \frac {a^{12} x^{25}}{25}+\frac {6}{25} a^{11} b x^{50}+\frac {22}{25} a^{10} b^2 x^{75}+\frac {11}{5} a^9 b^3 x^{100}+\frac {99}{25} a^8 b^4 x^{125}+\frac {132}{25} a^7 b^5 x^{150}+\frac {132}{25} a^6 b^6 x^{175}+\frac {99}{25} a^5 b^7 x^{200}+\frac {11}{5} a^4 b^8 x^{225}+\frac {22}{25} a^3 b^9 x^{250}+\frac {6}{25} a^2 b^{10} x^{275}+\frac {1}{25} a b^{11} x^{300}+\frac {b^{12} x^{325}}{325} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{24} \left (a+b x^{25}\right )^{12} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.35, size = 134, normalized size = 8.38 \begin {gather*} \frac {1}{325} x^{325} b^{12} + \frac {1}{25} x^{300} b^{11} a + \frac {6}{25} x^{275} b^{10} a^{2} + \frac {22}{25} x^{250} b^{9} a^{3} + \frac {11}{5} x^{225} b^{8} a^{4} + \frac {99}{25} x^{200} b^{7} a^{5} + \frac {132}{25} x^{175} b^{6} a^{6} + \frac {132}{25} x^{150} b^{5} a^{7} + \frac {99}{25} x^{125} b^{4} a^{8} + \frac {11}{5} x^{100} b^{3} a^{9} + \frac {22}{25} x^{75} b^{2} a^{10} + \frac {6}{25} x^{50} b a^{11} + \frac {1}{25} x^{25} a^{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 14, normalized size = 0.88 \begin {gather*} \frac {{\left (b x^{25} + a\right )}^{13}}{325 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.04, size = 135, normalized size = 8.44 \begin {gather*} \frac {1}{325} b^{12} x^{325}+\frac {1}{25} a \,b^{11} x^{300}+\frac {6}{25} a^{2} b^{10} x^{275}+\frac {22}{25} a^{3} b^{9} x^{250}+\frac {11}{5} a^{4} b^{8} x^{225}+\frac {99}{25} a^{5} b^{7} x^{200}+\frac {132}{25} a^{6} b^{6} x^{175}+\frac {132}{25} a^{7} b^{5} x^{150}+\frac {99}{25} a^{8} b^{4} x^{125}+\frac {11}{5} a^{9} b^{3} x^{100}+\frac {22}{25} a^{10} b^{2} x^{75}+\frac {6}{25} a^{11} b \,x^{50}+\frac {1}{25} a^{12} x^{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.35, size = 14, normalized size = 0.88 \begin {gather*} \frac {{\left (b x^{25} + a\right )}^{13}}{325 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.20, size = 14, normalized size = 0.88 \begin {gather*} \frac {{\left (b\,x^{25}+a\right )}^{13}}{325\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.11, size = 160, normalized size = 10.00 \begin {gather*} \frac {a^{12} x^{25}}{25} + \frac {6 a^{11} b x^{50}}{25} + \frac {22 a^{10} b^{2} x^{75}}{25} + \frac {11 a^{9} b^{3} x^{100}}{5} + \frac {99 a^{8} b^{4} x^{125}}{25} + \frac {132 a^{7} b^{5} x^{150}}{25} + \frac {132 a^{6} b^{6} x^{175}}{25} + \frac {99 a^{5} b^{7} x^{200}}{25} + \frac {11 a^{4} b^{8} x^{225}}{5} + \frac {22 a^{3} b^{9} x^{250}}{25} + \frac {6 a^{2} b^{10} x^{275}}{25} + \frac {a b^{11} x^{300}}{25} + \frac {b^{12} x^{325}}{325} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________