\(\int \frac {\tanh (e+f x)}{c+d x} \, dx\) [4]

Optimal result

Integrand size = 14, antiderivative size = 14 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\text {Int}\left (\frac {\tanh (e+f x)}{c+d x},x\right ) \]

[Out]

Unintegrable(tanh(f*x+e)/(d*x+c),x)

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int \frac {\tanh (e+f x)}{c+d x} \, dx \]

[In]

Int[Tanh[e + f*x]/(c + d*x),x]

[Out]

Defer[Int][Tanh[e + f*x]/(c + d*x), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\tanh (e+f x)}{c+d x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 9.68 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int \frac {\tanh (e+f x)}{c+d x} \, dx \]

[In]

Integrate[Tanh[e + f*x]/(c + d*x),x]

[Out]

Integrate[Tanh[e + f*x]/(c + d*x), x]

Maple [N/A] (verified)

Not integrable

Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00

\[\int \frac {\tanh \left (f x +e \right )}{d x +c}d x\]

[In]

int(tanh(f*x+e)/(d*x+c),x)

[Out]

int(tanh(f*x+e)/(d*x+c),x)

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int { \frac {\tanh \left (f x + e\right )}{d x + c} \,d x } \]

[In]

integrate(tanh(f*x+e)/(d*x+c),x, algorithm="fricas")

[Out]

integral(tanh(f*x + e)/(d*x + c), x)

Sympy [N/A]

Not integrable

Time = 0.42 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int \frac {\tanh {\left (e + f x \right )}}{c + d x}\, dx \]

[In]

integrate(tanh(f*x+e)/(d*x+c),x)

[Out]

Integral(tanh(e + f*x)/(c + d*x), x)

Maxima [N/A]

Not integrable

Time = 0.41 (sec) , antiderivative size = 42, normalized size of antiderivative = 3.00 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int { \frac {\tanh \left (f x + e\right )}{d x + c} \,d x } \]

[In]

integrate(tanh(f*x+e)/(d*x+c),x, algorithm="maxima")

[Out]

log(d*x + c)/d - 2*integrate(1/(d*x + (d*x*e^(2*e) + c*e^(2*e))*e^(2*f*x) + c), x)

Giac [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int { \frac {\tanh \left (f x + e\right )}{d x + c} \,d x } \]

[In]

integrate(tanh(f*x+e)/(d*x+c),x, algorithm="giac")

[Out]

integrate(tanh(f*x + e)/(d*x + c), x)

Mupad [N/A]

Not integrable

Time = 1.68 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\tanh (e+f x)}{c+d x} \, dx=\int \frac {\mathrm {tanh}\left (e+f\,x\right )}{c+d\,x} \,d x \]

[In]

int(tanh(e + f*x)/(c + d*x),x)

[Out]

int(tanh(e + f*x)/(c + d*x), x)