3.112 \(\int \frac{1}{x^3 \log ^2(c (a+b x^2)^p)} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x^3 \log ^2\left (c \left (a+b x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable[1/(x^3*Log[c*(a + b*x^2)^p]^2), x]

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Rubi [A]  time = 0.0172644, 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 = {} \[ \int \frac{1}{x^3 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^3*Log[c*(a + b*x^2)^p]^2),x]

[Out]

Defer[Int][1/(x^3*Log[c*(a + b*x^2)^p]^2), x]

Rubi steps

\begin{align*} \int \frac{1}{x^3 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx &=\int \frac{1}{x^3 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx\\ \end{align*}

Mathematica [A]  time = 1.45958, size = 0, normalized size = 0. \[ \int \frac{1}{x^3 \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^3*Log[c*(a + b*x^2)^p]^2),x]

[Out]

Integrate[1/(x^3*Log[c*(a + b*x^2)^p]^2), x]

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Maple [A]  time = 3.458, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{3} \left ( \ln \left ( c \left ( b{x}^{2}+a \right ) ^{p} \right ) \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^3/ln(c*(b*x^2+a)^p)^2,x)

[Out]

int(1/x^3/ln(c*(b*x^2+a)^p)^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{b x^{2} + a}{2 \,{\left (b p x^{4} \log \left ({\left (b x^{2} + a\right )}^{p}\right ) + b p x^{4} \log \left (c\right )\right )}} - \int \frac{b x^{2} + 2 \, a}{b p x^{5} \log \left ({\left (b x^{2} + a\right )}^{p}\right ) + b p x^{5} \log \left (c\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^3/log(c*(b*x^2+a)^p)^2,x, algorithm="maxima")

[Out]

-1/2*(b*x^2 + a)/(b*p*x^4*log((b*x^2 + a)^p) + b*p*x^4*log(c)) - integrate((b*x^2 + 2*a)/(b*p*x^5*log((b*x^2 +
a)^p) + b*p*x^5*log(c)), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x^{3} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^3/log(c*(b*x^2+a)^p)^2,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{3} \log{\left (c \left (a + b x^{2}\right )^{p} \right )}^{2}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**3/ln(c*(b*x**2+a)**p)**2,x)

[Out]

Integral(1/(x**3*log(c*(a + b*x**2)**p)**2), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{3} \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^3/log(c*(b*x^2+a)^p)^2,x, algorithm="giac")

[Out]

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