3.175 \(\int (c+e x^2)^q (a+b x^4)^p \, dx\)

Optimal. Leaf size=21 \[ \text{Unintegrable}\left (\left (a+b x^4\right )^p \left (c+e x^2\right )^q,x\right ) \]

[Out]

Defer[Int][(c + e*x^2)^q*(a + b*x^4)^p, x]

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Rubi [A]  time = 0.0080599, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Int[(c + e*x^2)^q*(a + b*x^4)^p,x]

[Out]

Defer[Int][(c + e*x^2)^q*(a + b*x^4)^p, x]

Rubi steps

\begin{align*} \int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx &=\int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx\\ \end{align*}

Mathematica [A]  time = 0.0762001, size = 0, normalized size = 0. \[ \int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(c + e*x^2)^q*(a + b*x^4)^p,x]

[Out]

Integrate[(c + e*x^2)^q*(a + b*x^4)^p, x]

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Maple [A]  time = 0.102, size = 0, normalized size = 0. \begin{align*} \int \left ( e{x}^{2}+c \right ) ^{q} \left ( b{x}^{4}+a \right ) ^{p}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x^2+c)^q*(b*x^4+a)^p,x)

[Out]

int((e*x^2+c)^q*(b*x^4+a)^p,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b x^{4} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x^2+c)^q*(b*x^4+a)^p,x, algorithm="maxima")

[Out]

integrate((b*x^4 + a)^p*(e*x^2 + c)^q, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (b x^{4} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x^2+c)^q*(b*x^4+a)^p,x, algorithm="fricas")

[Out]

integral((b*x^4 + a)^p*(e*x^2 + c)^q, x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x**2+c)**q*(b*x**4+a)**p,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b x^{4} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x^2+c)^q*(b*x^4+a)^p,x, algorithm="giac")

[Out]

integrate((b*x^4 + a)^p*(e*x^2 + c)^q, x)