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

Optimal. Leaf size=35 \[ \text{Unintegrable}\left (\frac{i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.298996, 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 = {} \[ \int \frac{i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin{align*} \int \frac{544+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx &=\int \frac{544+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx\\ \end{align*}

Mathematica [A]  time = 2.98509, size = 0, normalized size = 0. \[ \int \frac{i+j x}{(g+h x) \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.626, size = 0, normalized size = 0. \begin{align*} \int{\frac{jx+i}{ \left ( hx+g \right ) \left ( a+b\ln \left ( c \left ( d \left ( fx+e \right ) ^{p} \right ) ^{q} \right ) \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{f j x^{2} + e i +{\left (f i + e j\right )} x}{a b f g p q +{\left (f g p q \log \left (c\right ) + f g p q \log \left (d^{q}\right )\right )} b^{2} +{\left (a b f h p q +{\left (f h p q \log \left (c\right ) + f h p q \log \left (d^{q}\right )\right )} b^{2}\right )} x +{\left (b^{2} f h p q x + b^{2} f g p q\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )} + \int \frac{f h j x^{2} + 2 \, f g j x + f g i -{\left (h i - g j\right )} e}{a b f g^{2} p q +{\left (f g^{2} p q \log \left (c\right ) + f g^{2} p q \log \left (d^{q}\right )\right )} b^{2} +{\left (a b f h^{2} p q +{\left (f h^{2} p q \log \left (c\right ) + f h^{2} p q \log \left (d^{q}\right )\right )} b^{2}\right )} x^{2} + 2 \,{\left (a b f g h p q +{\left (f g h p q \log \left (c\right ) + f g h p q \log \left (d^{q}\right )\right )} b^{2}\right )} x +{\left (b^{2} f h^{2} p q x^{2} + 2 \, b^{2} f g h p q x + b^{2} f g^{2} p q\right )} \log \left ({\left ({\left (f x + e\right )}^{p}\right )}^{q}\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{j x + i}{a^{2} h x + a^{2} g +{\left (b^{2} h x + b^{2} g\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )^{2} + 2 \,{\left (a b h x + a b g\right )} \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{j x + i}{{\left (h x + g\right )}{\left (b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a\right )}^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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