3.275 \(\int \frac {\log ^2(c (d+e x^2)^p)}{f+g x^2} \, dx\)

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2},x\right ) \]

[Out]

Unintegrable(ln(c*(e*x^2+d)^p)^2/(g*x^2+f),x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[c*(d + e*x^2)^p]^2/(f + g*x^2),x]

[Out]

Defer[Int][Log[c*(d + e*x^2)^p]^2/(f + g*x^2), x]

Rubi steps

\begin {align*} \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx &=\int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 2.84, size = 0, normalized size = 0.00 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^2),x]

[Out]

Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^2), x]

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fricas [A]  time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{g x^{2} + f}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f),x, algorithm="fricas")

[Out]

integral(log((e*x^2 + d)^p*c)^2/(g*x^2 + f), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f),x, algorithm="giac")

[Out]

integrate(log((e*x^2 + d)^p*c)^2/(g*x^2 + f), x)

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maple [A]  time = 18.03, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}{g \,x^{2}+f}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(c*(e*x^2+d)^p)^2/(g*x^2+f),x)

[Out]

int(ln(c*(e*x^2+d)^p)^2/(g*x^2+f),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f),x, algorithm="maxima")

[Out]

integrate(log((e*x^2 + d)^p*c)^2/(g*x^2 + f), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(c*(d + e*x^2)^p)^2/(f + g*x^2),x)

[Out]

int(log(c*(d + e*x^2)^p)^2/(f + g*x^2), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log {\left (c \left (d + e x^{2}\right )^{p} \right )}^{2}}{f + g x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(c*(e*x**2+d)**p)**2/(g*x**2+f),x)

[Out]

Integral(log(c*(d + e*x**2)**p)**2/(f + g*x**2), x)

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