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=34 \[ \text{Unintegrable}\left (\frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.110533, 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 = {} \[ \int \frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \]

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*}

Mathematica [A]  time = 0.602643, size = 0, normalized size = 0. \[ \int \frac{(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \]

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]

________________________________________________________________________________________

Maple [A]  time = 1.629, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( ix+h \right ) ^{q} \left ( a+b\ln \left ( c \left ( fx+e \right ) \right ) \right ) ^{p}}{dfx+de}}\, dx \end{align*}

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)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \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} \end{align*}

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)

________________________________________________________________________________________

Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

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]

Exception raised: UnboundLocalError

________________________________________________________________________________________

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

[Out]

Timed out

________________________________________________________________________________________

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

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