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

Optimal. Leaf size=22 \[ \text {Int}\left (\left (a+b x^4\right )^p \left (c+e x^2\right )^q,x\right ) \]

[Out]

Unintegrable((e*x^2+c)^q*(b*x^4+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 = {} \[ \int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx \]

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*}

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Mathematica [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int \left (c+e x^2\right )^q \left (a+b x^4\right )^p \, dx \]

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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fricas [A]  time = 1.07, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b x^{4} + a\right )}^{p} {\left (e x^{2} + c\right )}^{q}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b x^{4} + a\right )}^{p} {\left (e x^{2} + c\right )}^{q}\,{d x} \]

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)

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maple [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \left (b \,x^{4}+a \right )^{p} \left (e \,x^{2}+c \right )^{q}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b x^{4} + a\right )}^{p} {\left (e x^{2} + c\right )}^{q}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int {\left (b\,x^4+a\right )}^p\,{\left (e\,x^2+c\right )}^q \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x^4)^p*(c + e*x^2)^q,x)

[Out]

int((a + b*x^4)^p*(c + e*x^2)^q, x)

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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]

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

[Out]

Timed out

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