Optimal. Leaf size=23 \[ \text {Int}\left ((c+d x)^m (a \tanh (e+f x)+a)^2,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, 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 = {} \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx &=\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 34.65, size = 0, normalized size = 0.00 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.53, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (a^{2} \tanh \left (f x + e\right )^{2} + 2 \, a^{2} \tanh \left (f x + e\right ) + a^{2}\right )} {\left (d x + c\right )}^{m}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.26, size = 0, normalized size = 0.00 \[ \int \left (d x +c \right )^{m} \left (a +a \tanh \left (f x +e \right )\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {{\left (d x + c\right )}^{m + 1} a^{2}}{d {\left (m + 1\right )}} + \int \frac {2 \, {\left (d x + c\right )}^{m} a^{2} {\left (e^{\left (f x + e\right )} - e^{\left (-f x - e\right )}\right )}}{e^{\left (f x + e\right )} + e^{\left (-f x - e\right )}} + \frac {{\left (d x + c\right )}^{m} a^{2} {\left (e^{\left (f x + e\right )} - e^{\left (-f x - e\right )}\right )}^{2}}{{\left (e^{\left (f x + e\right )} + e^{\left (-f x - e\right )}\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int {\left (a+a\,\mathrm {tanh}\left (e+f\,x\right )\right )}^2\,{\left (c+d\,x\right )}^m \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ a^{2} \left (\int 2 \left (c + d x\right )^{m} \tanh {\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m} \tanh ^{2}{\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________