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

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

[Out]

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

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Rubi [A]  time = 0.11, 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 = {} \[ \int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {align*} \int \frac {(h+209 x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx &=\int \frac {(h+209 x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.62, size = 0, normalized size = 0.00 \[ \int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (i x + h\right )}^{q} {\left (b \log \left (c f x + c e\right ) + a\right )}^{p}}{d f x + d e}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Simplification as
suming c near 0Simplification assuming f near 0Simplification assuming t_nostep near 0Simplification assuming
c near 0Simplification assuming f near 0Simplification assuming t_nostep near 0Simplification assuming c near
0Simplification assuming f near 0Simplification assuming t_nostep near 0Simplification assuming c near 0Simpli
fication assuming f near 0Simplification assuming t_nostep near 0Simplification assuming c near 0Simplificatio
n assuming f near 0Simplification assuming x near 0Simplification assuming c near 0Simplification assuming f n
ear 0Simplification assuming x near 0Evaluation time: 0.78Unable to divide, perhaps due to rounding error%%%{-
i,[0,0,5,0,2,0,0,3,0,2,0]%%%}+%%%{-5,[0,0,4,0,2,0,1,3,0,2,0]%%%}+%%%{10*i,[0,0,3,0,2,0,2,3,0,2,0]%%%}+%%%{10,[
0,0,2,0,2,0,3,3,0,2,0]%%%}+%%%{-5*i,[0,0,1,0,2,0,4,3,0,2,0]%%%}+%%%{-1,[0,0,0,0,2,0,5,3,0,2,0]%%%} / %%%{-i,[0
,0,6,0,3,0,0,3,0,2,0]%%%}+%%%{-5,[0,0,5,0,3,0,1,3,0,2,0]%%%}+%%%{-i,[0,0,5,0,2,1,0,3,0,2,0]%%%}+%%%{10*i,[0,0,
4,0,3,0,2,3,0,2,0]%%%}+%%%{-5,[0,0,4,0,2,1,1,3,0,2,0]%%%}+%%%{10,[0,0,3,0,3,0,3,3,0,2,0]%%%}+%%%{10*i,[0,0,3,0
,2,1,2,3,0,2,0]%%%}+%%%{-5*i,[0,0,2,0,3,0,4,3,0,2,0]%%%}+%%%{10,[0,0,2,0,2,1,3,3,0,2,0]%%%}+%%%{-1,[0,0,1,0,3,
0,5,3,0,2,0]%%%}+%%%{-5*i,[0,0,1,0,2,1,4,3,0,2,0]%%%}+%%%{-1,[0,0,0,0,2,1,5,3,0,2,0]%%%} Error: Bad Argument V
alue

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maple [A]  time = 0.88, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (\left (f x +e \right ) c \right )+a \right )^{p} \left (i x +h \right )^{q}}{d f x +d e}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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