3.4.28 \(\int \frac {1}{(d+e x^3)^2 (a+b \log (c x^n))^2} \, dx\) [328]

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2},x\right ) \]

[Out]

Unintegrable(1/(e*x^3+d)^2/(a+b*ln(c*x^n))^2,x)

________________________________________________________________________________________

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 = {} \begin {gather*} \int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((d + e*x^3)^2*(a + b*Log[c*x^n])^2),x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 19.22, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (e \,x^{3}+d \right )^{2} \left (a +b \ln \left (c \,x^{n}\right )\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(1/(e*x^3+d)^2/(a+b*ln(c*x^n))^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/(e*x^3+d)^2/(a+b*log(c*x^n))^2,x, algorithm="maxima")

[Out]

-x/((b^2*n*log(c) + a*b*n)*x^6*e^2 + b^2*d^2*n*log(c) + a*b*d^2*n + 2*(b^2*d*n*log(c) + a*b*d*n)*x^3*e + (b^2*
n*x^6*e^2 + 2*b^2*d*n*x^3*e + b^2*d^2*n)*log(x^n)) - integrate((5*x^3*e - d)/((b^2*n*log(c) + a*b*n)*x^9*e^3 +
3*(b^2*d*n*log(c) + a*b*d*n)*x^6*e^2 + b^2*d^3*n*log(c) + a*b*d^3*n + 3*(b^2*d^2*n*log(c) + a*b*d^2*n)*x^3*e
+ (b^2*n*x^9*e^3 + 3*b^2*d*n*x^6*e^2 + 3*b^2*d^2*n*x^3*e + b^2*d^3*n)*log(x^n)), x)

________________________________________________________________________________________

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/(e*x^3+d)^2/(a+b*log(c*x^n))^2,x, algorithm="fricas")

[Out]

integral(1/(a^2*x^6*e^2 + 2*a^2*d*x^3*e + a^2*d^2 + (b^2*x^6*e^2 + 2*b^2*d*x^3*e + b^2*d^2)*log(c*x^n)^2 + 2*(
a*b*x^6*e^2 + 2*a*b*d*x^3*e + a*b*d^2)*log(c*x^n)), x)

________________________________________________________________________________________

Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x**3+d)**2/(a+b*ln(c*x**n))**2,x)

[Out]

Timed out

________________________________________________________________________________________

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/(e*x^3+d)^2/(a+b*log(c*x^n))^2,x, algorithm="giac")

[Out]

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

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{{\left (e\,x^3+d\right )}^2\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((d + e*x^3)^2*(a + b*log(c*x^n))^2),x)

[Out]

int(1/((d + e*x^3)^2*(a + b*log(c*x^n))^2), x)

________________________________________________________________________________________