\(\int \frac {\log ^2(c (d+e x^2)^p)}{(f+g x^3)^2} \, dx\) [297]

Optimal result

Integrand size = 24, antiderivative size = 24 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\text {Int}\left (\frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx \]

[In]

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

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 26.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx \]

[In]

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

[Out]

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

Maple [N/A]

Not integrable

Time = 0.83 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.54 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\int { \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{{\left (g x^{3} + f\right )}^{2}} \,d x } \]

[In]

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

[Out]

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

Sympy [F(-1)]

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

[In]

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

[Out]

Timed out

Maxima [F(-2)]

Exception generated. \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\text {Exception raised: ValueError} \]

[In]

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

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(e>0)', see `assume?` for more
details)Is e

Giac [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\int { \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{{\left (g x^{3} + f\right )}^{2}} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 1.43 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx=\int \frac {{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2}{{\left (g\,x^3+f\right )}^2} \,d x \]

[In]

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

[Out]

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