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

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

[Out]

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

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

Verification is Not applicable to the result.

[In]

Int[x^2/Log[c*(a + b*x^2)^p]^2,x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.35, size = 0, normalized size = 0.00 \[ \int \frac {x^2}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{2}}{\log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 3.52, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*(b*x^3 + a*x)/(b*p^2*log(b*x^2 + a) + b*p*log(c)) + integrate(1/2*(3*b*x^2 + a)/(b*p^2*log(b*x^2 + a) + b
*p*log(c)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/log(c*(a + b*x^2)^p)^2,x)

[Out]

int(x^2/log(c*(a + b*x^2)^p)^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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