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

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

[Out]

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

Verification is Not applicable to the result.

[In]

Int[1/(x^2*Log[c*(a + b*x^2)^p]),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.42, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \log \left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.50, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \ln \left (c \left (b \,x^{2}+a \right )^{p}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*log(c*(a + b*x^2)^p)),x)

[Out]

int(1/(x^2*log(c*(a + b*x^2)^p)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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