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

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x^2 \log \left (c \left (a+b x^2\right )^p\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0177068, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}

Mathematica [A]  time = 0.396934, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \log \left (c \left (a+b x^2\right )^p\right )} \, dx \]

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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Maple [A]  time = 0.472, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2}\ln \left ( c \left ( b{x}^{2}+a \right ) ^{p} \right ) }}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )}\,{d x} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x^{2} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )}, x\right ) \end{align*}

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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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \log{\left (c \left (a + b x^{2}\right )^{p} \right )}}\, dx \end{align*}

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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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )}\,{d x} \end{align*}

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)