3.4.6 \(\int \frac {(f+g x^3)^2}{\log ^2(c (d+e x^2)^p)} \, dx\) [306]

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\left (f+g x^3\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable((g*x^3+f)^2/ln(c*(e*x^2+d)^p)^2,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 \frac {\left (f+g x^3\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2,x]

[Out]

Defer[Int][(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2, x]

Rubi steps

\begin {align*} \int \frac {\left (f+g x^3\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac {\left (f+g x^3\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.42, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (f+g x^3\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2,x]

[Out]

Integrate[(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2, x]

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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (g \,x^{3}+f \right )^{2}}{\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((g*x^3+f)^2/ln(c*(e*x^2+d)^p)^2,x)

[Out]

int((g*x^3+f)^2/ln(c*(e*x^2+d)^p)^2,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((g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm="maxima")

[Out]

-1/2*(g^2*x^8*e + d*g^2*x^6 + 2*f*g*x^5*e + 2*d*f*g*x^3 + f^2*x^2*e + d*f^2)/(p^2*x*e*log(x^2*e + d) + p*x*e*l
og(c)) + integrate(1/2*(7*g^2*x^8*e + 5*d*g^2*x^6 + 8*f*g*x^5*e + 4*d*f*g*x^3 + f^2*x^2*e - d*f^2)/(p^2*x^2*e*
log(x^2*e + d) + p*x^2*e*log(c)), 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((g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm="fricas")

[Out]

integral((g^2*x^6 + 2*f*g*x^3 + f^2)/log((x^2*e + d)^p*c)^2, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (f + g x^{3}\right )^{2}}{\log {\left (c \left (d + e x^{2}\right )^{p} \right )}^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x**3+f)**2/ln(c*(e*x**2+d)**p)**2,x)

[Out]

Integral((f + g*x**3)**2/log(c*(d + e*x**2)**p)**2, x)

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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((g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm="giac")

[Out]

integrate((g*x^3 + f)^2/log((x^2*e + d)^p*c)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (g\,x^3+f\right )}^2}{{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((f + g*x^3)^2/log(c*(d + e*x^2)^p)^2,x)

[Out]

int((f + g*x^3)^2/log(c*(d + e*x^2)^p)^2, x)

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