3.2.14 \(\int \frac {1}{\log ^2(c (a+b x^2)^p)} \, dx\) [114]

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{\log ^2\left (c \left (a+b x^2\right )^p\right )},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.00, 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 = {} \begin {gather*} \int \frac {1}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Log[c*(a + b*x^2)^p]^(-2),x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.27, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {1}{{\ln \left (c\,{\left (b\,x^2+a\right )}^p\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/log(c*(a + b*x^2)^p)^2,x)

[Out]

int(1/log(c*(a + b*x^2)^p)^2, x)

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