3.60 \(\int \frac {\log (e (f (a+b x)^p (c+d x)^q)^r)}{x \log (i (j (h x)^t)^u)} \, dx\)

Optimal. Leaf size=42 \[ \text {Int}\left (\frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log \left (i \left (j (h x)^t\right )^u\right )},x\right ) \]

[Out]

CannotIntegrate(ln(e*(f*(b*x+a)^p*(d*x+c)^q)^r)/x/ln(i*(j*(h*x)^t)^u),x)

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Rubi [A]  time = 0.54, 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 = {} \[ \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log \left (i \left (j (h x)^t\right )^u\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {align*} \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log \left (60 \left (j (h x)^t\right )^u\right )} \, dx &=\int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log \left (60 \left (j (h x)^t\right )^u\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.49, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log \left (i \left (j (h x)^t\right )^u\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.67, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (\left ({\left (b x + a\right )}^{p} {\left (d x + c\right )}^{q} f\right )^{r} e\right )}{x \log \left (\left (\left (h x\right )^{t} j\right )^{u} i\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 1.69, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (e \left (f \left (b x +a \right )^{p} \left (d x +c \right )^{q}\right )^{r}\right )}{x \ln \left (i \left (j \left (h x \right )^{t}\right )^{u}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {\ln \left (e\,{\left (f\,{\left (a+b\,x\right )}^p\,{\left (c+d\,x\right )}^q\right )}^r\right )}{x\,\ln \left (i\,{\left (j\,{\left (h\,x\right )}^t\right )}^u\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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