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

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

[Out]

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

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Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \]

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*}

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Mathematica [A]  time = 0.30, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (d+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \]

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]

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fricas [A]  time = 0.70, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (e {\left (f^{b c x + a c}\right )}^{n} + d\right )}{x}, x\right ) \]

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)

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

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)

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maple [A]  time = 0.24, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (e \left (f^{\left (b x +a \right ) c}\right )^{n}+d \right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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)

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

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)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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