3.3.9 \(\int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx\) [209]

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 = 0.08, 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 {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \end {gather*}

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 = 0.51, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \end {gather*}

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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Maple [A]
time = 0.26, size = 0, normalized size = 0.00 \[\int \frac {\left (i x +h \right )^{q} \left (a +b \ln \left (c \left (f x +e \right )\right )\right )^{p}}{d f x +e d}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

[Out]

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

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

[Out]

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

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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((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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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

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 sageVARc near 0Simplification assuming sageVARf near 0Simplification assuming t_nostep near 0Simplifica
tion assuming

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \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 \end {gather*}

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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