3.547 \(\int \frac {1}{(g+h x) (i+j x)^2 (a+b \log (c (d (e+f x)^p)^q))^2} \, dx\)

Optimal. Leaf size=38 \[ \text {Int}\left (\frac {1}{(g+h x) (i+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2},x\right ) \]

[Out]

Unintegrable(1/(h*x+g)/(j*x+i)^2/(a+b*ln(c*(d*(f*x+e)^p)^q))^2,x)

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Rubi [A]  time = 0.33, 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 = {} \[ \int \frac {1}{(g+h x) (i+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]

[Out]

Defer[Int][1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]

Rubi steps

\begin {align*} \int \frac {1}{(g+h x) (547+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx &=\int \frac {1}{(g+h x) (547+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 42.96, size = 0, normalized size = 0.00 \[ \int \frac {1}{(g+h x) (i+j x)^2 \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2),x]

[Out]

Integrate[1/((g + h*x)*(i + j*x)^2*(a + b*Log[c*(d*(e + f*x)^p)^q])^2), x]

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fricas [A]  time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a^{2} h j^{2} x^{3} + a^{2} g i^{2} + {\left (2 \, a^{2} h i j + a^{2} g j^{2}\right )} x^{2} + {\left (b^{2} h j^{2} x^{3} + b^{2} g i^{2} + {\left (2 \, b^{2} h i j + b^{2} g j^{2}\right )} x^{2} + {\left (b^{2} h i^{2} + 2 \, b^{2} g i j\right )} x\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + {\left (a^{2} h i^{2} + 2 \, a^{2} g i j\right )} x + 2 \, {\left (a b h j^{2} x^{3} + a b g i^{2} + {\left (2 \, a b h i j + a b g j^{2}\right )} x^{2} + {\left (a b h i^{2} + 2 \, a b g i j\right )} x\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(h*x+g)/(j*x+i)^2/(a+b*log(c*(d*(f*x+e)^p)^q))^2,x, algorithm="fricas")

[Out]

integral(1/(a^2*h*j^2*x^3 + a^2*g*i^2 + (2*a^2*h*i*j + a^2*g*j^2)*x^2 + (b^2*h*j^2*x^3 + b^2*g*i^2 + (2*b^2*h*
i*j + b^2*g*j^2)*x^2 + (b^2*h*i^2 + 2*b^2*g*i*j)*x)*log(((f*x + e)^p*d)^q*c)^2 + (a^2*h*i^2 + 2*a^2*g*i*j)*x +
2*(a*b*h*j^2*x^3 + a*b*g*i^2 + (2*a*b*h*i*j + a*b*g*j^2)*x^2 + (a*b*h*i^2 + 2*a*b*g*i*j)*x)*log(((f*x + e)^p*
d)^q*c)), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (h x + g\right )} {\left (j x + i\right )}^{2} {\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(h*x+g)/(j*x+i)^2/(a+b*log(c*(d*(f*x+e)^p)^q))^2,x, algorithm="giac")

[Out]

integrate(1/((h*x + g)*(j*x + i)^2*(b*log(((f*x + e)^p*d)^q*c) + a)^2), x)

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maple [A]  time = 0.55, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (h x +g \right ) \left (j x +i \right )^{2} \left (b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )+a \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(h*x+g)/(j*x+i)^2/(b*ln(c*(d*(f*x+e)^p)^q)+a)^2,x)

[Out]

int(1/(h*x+g)/(j*x+i)^2/(b*ln(c*(d*(f*x+e)^p)^q)+a)^2,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(h*x+g)/(j*x+i)^2/(a+b*log(c*(d*(f*x+e)^p)^q))^2,x, algorithm="maxima")

[Out]

-(f*x + e)/(a*b*f*g*i^2*p*q + (a*b*f*h*j^2*p*q + (f*h*j^2*p*q^2*log(d) + f*h*j^2*p*q*log(c))*b^2)*x^3 + (f*g*i
^2*p*q^2*log(d) + f*g*i^2*p*q*log(c))*b^2 + ((2*h*i*j*p*q + g*j^2*p*q)*a*b*f + ((2*h*i*j*p*q + g*j^2*p*q)*f*lo
g(c) + (2*h*i*j*p*q^2 + g*j^2*p*q^2)*f*log(d))*b^2)*x^2 + ((h*i^2*p*q + 2*g*i*j*p*q)*a*b*f + ((h*i^2*p*q + 2*g
*i*j*p*q)*f*log(c) + (h*i^2*p*q^2 + 2*g*i*j*p*q^2)*f*log(d))*b^2)*x + (b^2*f*h*j^2*p*q*x^3 + b^2*f*g*i^2*p*q +
(2*h*i*j*p*q + g*j^2*p*q)*b^2*f*x^2 + (h*i^2*p*q + 2*g*i*j*p*q)*b^2*f*x)*log(((f*x + e)^p)^q)) - integrate((2
*f*h*j*x^2 - f*g*i + (h*i + 2*g*j)*e + (f*g*j + 3*e*h*j)*x)/(a*b*f*g^2*i^3*p*q + (a*b*f*h^2*j^3*p*q + (f*h^2*j
^3*p*q^2*log(d) + f*h^2*j^3*p*q*log(c))*b^2)*x^5 + ((3*h^2*i*j^2*p*q + 2*g*h*j^3*p*q)*a*b*f + ((3*h^2*i*j^2*p*
q + 2*g*h*j^3*p*q)*f*log(c) + (3*h^2*i*j^2*p*q^2 + 2*g*h*j^3*p*q^2)*f*log(d))*b^2)*x^4 + ((3*h^2*i^2*j*p*q + 6
*g*h*i*j^2*p*q + g^2*j^3*p*q)*a*b*f + ((3*h^2*i^2*j*p*q + 6*g*h*i*j^2*p*q + g^2*j^3*p*q)*f*log(c) + (3*h^2*i^2
*j*p*q^2 + 6*g*h*i*j^2*p*q^2 + g^2*j^3*p*q^2)*f*log(d))*b^2)*x^3 + (f*g^2*i^3*p*q^2*log(d) + f*g^2*i^3*p*q*log
(c))*b^2 + ((h^2*i^3*p*q + 6*g*h*i^2*j*p*q + 3*g^2*i*j^2*p*q)*a*b*f + ((h^2*i^3*p*q + 6*g*h*i^2*j*p*q + 3*g^2*
i*j^2*p*q)*f*log(c) + (h^2*i^3*p*q^2 + 6*g*h*i^2*j*p*q^2 + 3*g^2*i*j^2*p*q^2)*f*log(d))*b^2)*x^2 + ((2*g*h*i^3
*p*q + 3*g^2*i^2*j*p*q)*a*b*f + ((2*g*h*i^3*p*q + 3*g^2*i^2*j*p*q)*f*log(c) + (2*g*h*i^3*p*q^2 + 3*g^2*i^2*j*p
*q^2)*f*log(d))*b^2)*x + (b^2*f*h^2*j^3*p*q*x^5 + b^2*f*g^2*i^3*p*q + (3*h^2*i*j^2*p*q + 2*g*h*j^3*p*q)*b^2*f*
x^4 + (3*h^2*i^2*j*p*q + 6*g*h*i*j^2*p*q + g^2*j^3*p*q)*b^2*f*x^3 + (h^2*i^3*p*q + 6*g*h*i^2*j*p*q + 3*g^2*i*j
^2*p*q)*b^2*f*x^2 + (2*g*h*i^3*p*q + 3*g^2*i^2*j*p*q)*b^2*f*x)*log(((f*x + e)^p)^q)), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {1}{\left (g+h\,x\right )\,{\left (i+j\,x\right )}^2\,{\left (a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((g + h*x)*(i + j*x)^2*(a + b*log(c*(d*(e + f*x)^p)^q))^2),x)

[Out]

int(1/((g + h*x)*(i + j*x)^2*(a + b*log(c*(d*(e + f*x)^p)^q))^2), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(h*x+g)/(j*x+i)**2/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)

[Out]

Timed out

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