### 3.122 $$\int \frac{\log (1+e (f^{c (a+b x)})^n)}{x} \, dx$$

Optimal. Leaf size=22 $\text{CannotIntegrate}\left (\frac{\log \left (e \left (f^{c (a+b x)}\right )^n+1\right )}{x},x\right )$

[Out]

CannotIntegrate[Log[1 + e*(f^(c*(a + b*x)))^n]/x, x]

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Rubi [A]  time = 0.0641357, 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 = {} $\int \frac{\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Log[1 + e*(f^(c*(a + b*x)))^n]/x,x]

[Out]

Defer[Int][Log[1 + e*(f^(c*(a + b*x)))^n]/x, x]

Rubi steps

\begin{align*} \int \frac{\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx &=\int \frac{\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.295591, size = 0, normalized size = 0. $\int \frac{\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Log[1 + e*(f^(c*(a + b*x)))^n]/x,x]

[Out]

Integrate[Log[1 + e*(f^(c*(a + b*x)))^n]/x, x]

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Maple [A]  time = 0.052, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( 1+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(1+e*(f^(c*(b*x+a)))^n)/x,x)

[Out]

int(ln(1+e*(f^(c*(b*x+a)))^n)/x,x)

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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} + 1\right )}{x}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(1+e*(f^(c*(b*x+a)))^n)/x,x, algorithm="maxima")

[Out]

integrate(log(e*(f^((b*x + a)*c))^n + 1)/x, x)

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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} + 1\right )}{x}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(1+e*(f^(c*(b*x+a)))^n)/x,x, algorithm="fricas")

[Out]

integral(log(e*(f^(b*c*x + a*c))^n + 1)/x, x)

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

[Out]

Timed out

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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} + 1\right )}{x}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(1+e*(f^(c*(b*x+a)))^n)/x,x, algorithm="giac")

[Out]

integrate(log(e*(f^((b*x + a)*c))^n + 1)/x, x)