\(\int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx\) [23]

Optimal result

Integrand size = 20, antiderivative size = 20 \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\text {Int}\left (\frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}},x\right ) \]

[Out]

Unintegrable((d*x+c)^2/(b*tanh(f*x+e))^(1/2),x)

Rubi [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx \]

[In]

Int[(c + d*x)^2/Sqrt[b*Tanh[e + f*x]],x]

[Out]

Defer[Int][(c + d*x)^2/Sqrt[b*Tanh[e + f*x]], x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx \\ \end{align*}

Mathematica [F(-1)]

Timed out. \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\text {\$Aborted} \]

[In]

Integrate[(c + d*x)^2/Sqrt[b*Tanh[e + f*x]],x]

[Out]

$Aborted

Maple [N/A] (verified)

Not integrable

Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90

\[\int \frac {\left (d x +c \right )^{2}}{\sqrt {b \tanh \left (f x +e \right )}}d x\]

[In]

int((d*x+c)^2/(b*tanh(f*x+e))^(1/2),x)

[Out]

int((d*x+c)^2/(b*tanh(f*x+e))^(1/2),x)

Fricas [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((d*x+c)^2/(b*tanh(f*x+e))^(1/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

Sympy [N/A]

Not integrable

Time = 1.25 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\int \frac {\left (c + d x\right )^{2}}{\sqrt {b \tanh {\left (e + f x \right )}}}\, dx \]

[In]

integrate((d*x+c)**2/(b*tanh(f*x+e))**(1/2),x)

[Out]

Integral((c + d*x)**2/sqrt(b*tanh(e + f*x)), x)

Maxima [N/A]

Not integrable

Time = 0.59 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\int { \frac {{\left (d x + c\right )}^{2}}{\sqrt {b \tanh \left (f x + e\right )}} \,d x } \]

[In]

integrate((d*x+c)^2/(b*tanh(f*x+e))^(1/2),x, algorithm="maxima")

[Out]

integrate((d*x + c)^2/sqrt(b*tanh(f*x + e)), x)

Giac [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate((d*x+c)^2/(b*tanh(f*x+e))^(1/2),x, algorithm="giac")

[Out]

Exception raised: RuntimeError >> an error occurred running a Giac command:INPUT:sage2OUTPUT:index.cc index_m
i_lex_is_greater Error: Bad Argument Value

Mupad [N/A]

Not integrable

Time = 2.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx=\int \frac {{\left (c+d\,x\right )}^2}{\sqrt {b\,\mathrm {tanh}\left (e+f\,x\right )}} \,d x \]

[In]

int((c + d*x)^2/(b*tanh(e + f*x))^(1/2),x)

[Out]

int((c + d*x)^2/(b*tanh(e + f*x))^(1/2), x)