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

Optimal. Leaf size=22 \[ \text{CannotIntegrate}\left (\frac{\log \left (e \left (f^{c (a+b x)}\right )^n+d\right )}{x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.0624786, 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 = {} \[ \int \frac{\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \]

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 = 0.289213, size = 0, normalized size = 0. \[ \int \frac{\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \]

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 = 0.05, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( d+e \left ({f}^{c \left ( bx+a \right ) } \right ) ^{n} \right ) }{x}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (e{\left (f^{{\left (b x + a\right )} c}\right )}^{n} + d\right )}{x}\,{d x} \end{align*}

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(e*(f^((b*x + a)*c))^n + d)/x, x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (e{\left (f^{b c x + a c}\right )}^{n} + d\right )}{x}, x\right ) \end{align*}

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(e*(f^(b*c*x + a*c))^n + d)/x, x)

________________________________________________________________________________________

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

[Out]

Timed out

________________________________________________________________________________________

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

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(e*(f^((b*x + a)*c))^n + d)/x, x)