3.4.99 \(\int (c+e x^2)^q (a+c x^2+b x^4)^p \, dx\) [399]

Optimal. Leaf size=27 \[ \text {Int}\left (\left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p,x\right ) \]

[Out]

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

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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*}

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Mathematica [A]
time = 0.09, size = 0, normalized size = 0.00 \begin {gather*} \int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.05, 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]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int {\left (e\,x^2+c\right )}^q\,{\left (b\,x^4+c\,x^2+a\right )}^p \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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