Optimal. Leaf size=27 \[ \text {Int}\left (\left (c+e x^2\right )^q \left (a+b x^4+c x^2\right )^p,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx &=\int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.10, size = 0, normalized size = 0.00 \[ \int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.22, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b x^{4} + c x^{2} + a\right )}^{p} {\left (e x^{2} + c\right )}^{q}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b x^{4} + c x^{2} + a\right )}^{p} {\left (e x^{2} + c\right )}^{q}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 0, normalized size = 0.00 \[ \int \left (e \,x^{2}+c \right )^{q} \left (b \,x^{4}+c \,x^{2}+a \right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b x^{4} + c x^{2} + a\right )}^{p} {\left (e x^{2} + c\right )}^{q}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int {\left (e\,x^2+c\right )}^q\,{\left (b\,x^4+c\,x^2+a\right )}^p \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________