3.2.11 \(\int \frac {1}{x \log ^2(c (a+b x^2)^p)} \, dx\) [111]

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

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.01, 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}{x \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/(x*Log[c*(a + b*x^2)^p]^2),x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 0.21, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \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/x/ln(c*(b*x**2+a)**p)**2,x)

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{x\,{\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/(x*log(c*(a + b*x^2)^p)^2),x)

[Out]

int(1/(x*log(c*(a + b*x^2)^p)^2), x)

________________________________________________________________________________________