Optimal. Leaf size=16 \[ \frac {1}{28} x^{28} \left (b+c x^2\right )^{14} \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {446, 74} \begin {gather*} \frac {1}{28} x^{28} \left (b+c x^2\right )^{14} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 74
Rule 446
Rubi steps
\begin {align*} \int x^{27} \left (b+c x^2\right )^{13} \left (b+2 c x^2\right ) \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int x^{13} (b+c x)^{13} (b+2 c x) \, dx,x,x^2\right )\\ &=\frac {1}{28} x^{28} \left (b+c x^2\right )^{14}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.01, size = 182, normalized size = 11.38 \begin {gather*} \frac {b^{14} x^{28}}{28}+\frac {1}{2} b^{13} c x^{30}+\frac {13}{4} b^{12} c^2 x^{32}+13 b^{11} c^3 x^{34}+\frac {143}{4} b^{10} c^4 x^{36}+\frac {143}{2} b^9 c^5 x^{38}+\frac {429}{4} b^8 c^6 x^{40}+\frac {858}{7} b^7 c^7 x^{42}+\frac {429}{4} b^6 c^8 x^{44}+\frac {143}{2} b^5 c^9 x^{46}+\frac {143}{4} b^4 c^{10} x^{48}+13 b^3 c^{11} x^{50}+\frac {13}{4} b^2 c^{12} x^{52}+\frac {1}{2} b c^{13} x^{54}+\frac {c^{14} x^{56}}{28} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{27} \left (b+c x^2\right )^{13} \left (b+2 c x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.36, size = 156, normalized size = 9.75 \begin {gather*} \frac {1}{28} x^{56} c^{14} + \frac {1}{2} x^{54} c^{13} b + \frac {13}{4} x^{52} c^{12} b^{2} + 13 x^{50} c^{11} b^{3} + \frac {143}{4} x^{48} c^{10} b^{4} + \frac {143}{2} x^{46} c^{9} b^{5} + \frac {429}{4} x^{44} c^{8} b^{6} + \frac {858}{7} x^{42} c^{7} b^{7} + \frac {429}{4} x^{40} c^{6} b^{8} + \frac {143}{2} x^{38} c^{5} b^{9} + \frac {143}{4} x^{36} c^{4} b^{10} + 13 x^{34} c^{3} b^{11} + \frac {13}{4} x^{32} c^{2} b^{12} + \frac {1}{2} x^{30} c b^{13} + \frac {1}{28} x^{28} b^{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.19, size = 156, normalized size = 9.75 \begin {gather*} \frac {1}{28} \, c^{14} x^{56} + \frac {1}{2} \, b c^{13} x^{54} + \frac {13}{4} \, b^{2} c^{12} x^{52} + 13 \, b^{3} c^{11} x^{50} + \frac {143}{4} \, b^{4} c^{10} x^{48} + \frac {143}{2} \, b^{5} c^{9} x^{46} + \frac {429}{4} \, b^{6} c^{8} x^{44} + \frac {858}{7} \, b^{7} c^{7} x^{42} + \frac {429}{4} \, b^{8} c^{6} x^{40} + \frac {143}{2} \, b^{9} c^{5} x^{38} + \frac {143}{4} \, b^{10} c^{4} x^{36} + 13 \, b^{11} c^{3} x^{34} + \frac {13}{4} \, b^{12} c^{2} x^{32} + \frac {1}{2} \, b^{13} c x^{30} + \frac {1}{28} \, b^{14} x^{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.04, size = 157, normalized size = 9.81 \begin {gather*} \frac {1}{28} c^{14} x^{56}+\frac {1}{2} b \,c^{13} x^{54}+\frac {13}{4} b^{2} c^{12} x^{52}+13 b^{3} c^{11} x^{50}+\frac {143}{4} b^{4} c^{10} x^{48}+\frac {143}{2} b^{5} c^{9} x^{46}+\frac {429}{4} b^{6} c^{8} x^{44}+\frac {858}{7} b^{7} c^{7} x^{42}+\frac {429}{4} b^{8} c^{6} x^{40}+\frac {143}{2} b^{9} c^{5} x^{38}+\frac {143}{4} b^{10} c^{4} x^{36}+13 b^{11} c^{3} x^{34}+\frac {13}{4} b^{12} c^{2} x^{32}+\frac {1}{2} b^{13} c \,x^{30}+\frac {1}{28} b^{14} x^{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.73, size = 156, normalized size = 9.75 \begin {gather*} \frac {1}{28} \, c^{14} x^{56} + \frac {1}{2} \, b c^{13} x^{54} + \frac {13}{4} \, b^{2} c^{12} x^{52} + 13 \, b^{3} c^{11} x^{50} + \frac {143}{4} \, b^{4} c^{10} x^{48} + \frac {143}{2} \, b^{5} c^{9} x^{46} + \frac {429}{4} \, b^{6} c^{8} x^{44} + \frac {858}{7} \, b^{7} c^{7} x^{42} + \frac {429}{4} \, b^{8} c^{6} x^{40} + \frac {143}{2} \, b^{9} c^{5} x^{38} + \frac {143}{4} \, b^{10} c^{4} x^{36} + 13 \, b^{11} c^{3} x^{34} + \frac {13}{4} \, b^{12} c^{2} x^{32} + \frac {1}{2} \, b^{13} c x^{30} + \frac {1}{28} \, b^{14} x^{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.93, size = 156, normalized size = 9.75 \begin {gather*} \frac {b^{14}\,x^{28}}{28}+\frac {b^{13}\,c\,x^{30}}{2}+\frac {13\,b^{12}\,c^2\,x^{32}}{4}+13\,b^{11}\,c^3\,x^{34}+\frac {143\,b^{10}\,c^4\,x^{36}}{4}+\frac {143\,b^9\,c^5\,x^{38}}{2}+\frac {429\,b^8\,c^6\,x^{40}}{4}+\frac {858\,b^7\,c^7\,x^{42}}{7}+\frac {429\,b^6\,c^8\,x^{44}}{4}+\frac {143\,b^5\,c^9\,x^{46}}{2}+\frac {143\,b^4\,c^{10}\,x^{48}}{4}+13\,b^3\,c^{11}\,x^{50}+\frac {13\,b^2\,c^{12}\,x^{52}}{4}+\frac {b\,c^{13}\,x^{54}}{2}+\frac {c^{14}\,x^{56}}{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.12, size = 182, normalized size = 11.38 \begin {gather*} \frac {b^{14} x^{28}}{28} + \frac {b^{13} c x^{30}}{2} + \frac {13 b^{12} c^{2} x^{32}}{4} + 13 b^{11} c^{3} x^{34} + \frac {143 b^{10} c^{4} x^{36}}{4} + \frac {143 b^{9} c^{5} x^{38}}{2} + \frac {429 b^{8} c^{6} x^{40}}{4} + \frac {858 b^{7} c^{7} x^{42}}{7} + \frac {429 b^{6} c^{8} x^{44}}{4} + \frac {143 b^{5} c^{9} x^{46}}{2} + \frac {143 b^{4} c^{10} x^{48}}{4} + 13 b^{3} c^{11} x^{50} + \frac {13 b^{2} c^{12} x^{52}}{4} + \frac {b c^{13} x^{54}}{2} + \frac {c^{14} x^{56}}{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________