3.2.27 \(\int \frac {\log (d+e (f^{c (a+b x)})^n)}{x} \, dx\) [127]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x},x\right ) \]

[Out]

CannotIntegrate(ln(d+e*(f^(c*(b*x+a)))^n)/x,x)

________________________________________________________________________________________

Rubi [A]
time = 0.04, 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 {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Log[d + e*(f^(c*(a + b*x)))^n]/x,x]

[Out]

Defer[Int][Log[d + e*(f^(c*(a + b*x)))^n]/x, x]

Rubi steps

\begin {align*} \int \frac {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx &=\int \frac {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.21, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Log[d + e*(f^(c*(a + b*x)))^n]/x,x]

[Out]

Integrate[Log[d + e*(f^(c*(a + b*x)))^n]/x, x]

________________________________________________________________________________________

Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (d +e \left (f^{c \left (b x +a \right )}\right )^{n}\right )}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(d+e*(f^(c*(b*x+a)))^n)/x,x)

[Out]

int(ln(d+e*(f^(c*(b*x+a)))^n)/x,x)

________________________________________________________________________________________

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(log(d+e*(f^(c*(b*x+a)))^n)/x,x, algorithm="maxima")

[Out]

integrate(log(f^((b*x + a)*c*n)*e + d)/x, x)

________________________________________________________________________________________

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(log(d+e*(f^(c*(b*x+a)))^n)/x,x, algorithm="fricas")

[Out]

integral(log((f^(b*c*x + a*c))^n*e + d)/x, x)

________________________________________________________________________________________

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(ln(d+e*(f**(c*(b*x+a)))**n)/x,x)

[Out]

Timed out

________________________________________________________________________________________

Giac [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(log(d+e*(f^(c*(b*x+a)))^n)/x,x, algorithm="giac")

[Out]

integrate(log((f^((b*x + a)*c))^n*e + d)/x, x)

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (d+e\,{\left (f^{c\,\left (a+b\,x\right )}\right )}^n\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(d + e*(f^(c*(a + b*x)))^n)/x,x)

[Out]

int(log(d + e*(f^(c*(a + b*x)))^n)/x, x)

________________________________________________________________________________________