3.120 \(\int \frac {x^2}{\log ^3(c (a+b x^2)^p)} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable(x^2/ln(c*(b*x^2+a)^p)^3,x)

________________________________________________________________________________________

Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^2/Log[c*(a + b*x^2)^p]^3,x]

[Out]

Defer[Int][x^2/Log[c*(a + b*x^2)^p]^3, x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.56, size = 0, normalized size = 0.00 \[ \int \frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^2/Log[c*(a + b*x^2)^p]^3,x]

[Out]

Integrate[x^2/Log[c*(a + b*x^2)^p]^3, x]

________________________________________________________________________________________

fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{2}}{\log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2/log(c*(b*x^2+a)^p)^3,x, algorithm="fricas")

[Out]

integral(x^2/log((b*x^2 + a)^p*c)^3, x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2/log(c*(b*x^2+a)^p)^3,x, algorithm="giac")

[Out]

integrate(x^2/log((b*x^2 + a)^p*c)^3, x)

________________________________________________________________________________________

maple [A]  time = 3.65, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/ln(c*(b*x^2+a)^p)^3,x)

[Out]

int(x^2/ln(c*(b*x^2+a)^p)^3,x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {b^{2} {\left (2 \, p + 3 \, \log \relax (c)\right )} x^{4} + 2 \, a b {\left (p + 2 \, \log \relax (c)\right )} x^{2} + a^{2} \log \relax (c) + {\left (3 \, b^{2} p x^{4} + 4 \, a b p x^{2} + a^{2} p\right )} \log \left (b x^{2} + a\right )}{8 \, {\left (b^{2} p^{4} x \log \left (b x^{2} + a\right )^{2} + 2 \, b^{2} p^{3} x \log \left (b x^{2} + a\right ) \log \relax (c) + b^{2} p^{2} x \log \relax (c)^{2}\right )}} + \int \frac {9 \, b^{2} x^{4} + 4 \, a b x^{2} - a^{2}}{8 \, {\left (b^{2} p^{3} x^{2} \log \left (b x^{2} + a\right ) + b^{2} p^{2} x^{2} \log \relax (c)\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2/log(c*(b*x^2+a)^p)^3,x, algorithm="maxima")

[Out]

-1/8*(b^2*(2*p + 3*log(c))*x^4 + 2*a*b*(p + 2*log(c))*x^2 + a^2*log(c) + (3*b^2*p*x^4 + 4*a*b*p*x^2 + a^2*p)*l
og(b*x^2 + a))/(b^2*p^4*x*log(b*x^2 + a)^2 + 2*b^2*p^3*x*log(b*x^2 + a)*log(c) + b^2*p^2*x*log(c)^2) + integra
te(1/8*(9*b^2*x^4 + 4*a*b*x^2 - a^2)/(b^2*p^3*x^2*log(b*x^2 + a) + b^2*p^2*x^2*log(c)), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {x^2}{{\ln \left (c\,{\left (b\,x^2+a\right )}^p\right )}^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/log(c*(a + b*x^2)^p)^3,x)

[Out]

int(x^2/log(c*(a + b*x^2)^p)^3, x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\log {\left (c \left (a + b x^{2}\right )^{p} \right )}^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2/ln(c*(b*x**2+a)**p)**3,x)

[Out]

Integral(x**2/log(c*(a + b*x**2)**p)**3, x)

________________________________________________________________________________________