3.115 \(\int \frac {1}{x^2 \log ^2(c (a+b x^2)^p)} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x^2 \log ^2\left (c \left (a+b x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable(1/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 = {} \[ \int \frac {1}{x^2 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*Log[c*(a + b*x^2)^p]^2),x]

[Out]

Defer[Int][1/(x^2*Log[c*(a + b*x^2)^p]^2), x]

Rubi steps

\begin {align*} \int \frac {1}{x^2 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx &=\int \frac {1}{x^2 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 1.25, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*Log[c*(a + b*x^2)^p]^2),x]

[Out]

Integrate[1/(x^2*Log[c*(a + b*x^2)^p]^2), x]

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/log(c*(b*x^2+a)^p)^2,x, algorithm="fricas")

[Out]

integral(1/(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 \[ \int \frac {1}{x^{2} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/log(c*(b*x^2+a)^p)^2,x, algorithm="giac")

[Out]

integrate(1/(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 \[ \int \frac {1}{x^{2} \ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/ln(c*(b*x^2+a)^p)^2,x)

[Out]

int(1/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 \[ -\frac {b x^{2} + a}{2 \, {\left (b p^{2} x^{3} \log \left (b x^{2} + a\right ) + b p x^{3} \log \relax (c)\right )}} - \int \frac {b x^{2} + 3 \, a}{2 \, {\left (b p^{2} x^{4} \log \left (b x^{2} + a\right ) + b p x^{4} \log \relax (c)\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/log(c*(b*x^2+a)^p)^2,x, algorithm="maxima")

[Out]

-1/2*(b*x^2 + a)/(b*p^2*x^3*log(b*x^2 + a) + b*p*x^3*log(c)) - integrate(1/2*(b*x^2 + 3*a)/(b*p^2*x^4*log(b*x^
2 + a) + b*p*x^4*log(c)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*log(c*(a + b*x^2)^p)^2),x)

[Out]

int(1/(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 \[ \int \frac {1}{x^{2} \log {\left (c \left (a + b x^{2}\right )^{p} \right )}^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/ln(c*(b*x**2+a)**p)**2,x)

[Out]

Integral(1/(x**2*log(c*(a + b*x**2)**p)**2), x)

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