3.404 \(\int \frac {(a+c x^2+b x^4)^p}{c+e x^2} \, dx\)

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

[Out]

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

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+c x^2+b x^4\right )^p}{c+e x^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b x^{4} + c x^{2} + a\right )}^{p}}{e x^{2} + c}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \,x^{4}+c \,x^{2}+a \right )^{p}}{e \,x^{2}+c}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (b\,x^4+c\,x^2+a\right )}^p}{e\,x^2+c} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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