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

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

[Out]

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

________________________________________________________________________________________

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

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 18.32, size = 0, normalized size = 0.00 \[ \int \frac {\log ^3\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^2\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.87, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{3}}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(log((e*x^2 + d)^p*c)^3/(g^2*x^4 + 2*f*g*x^2 + f^2), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maple [A]  time = 32.64, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{3}}{\left (g \,x^{2}+f \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

[Out]

Timed out

________________________________________________________________________________________