\(\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx\) [48]

Optimal result

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

[Out]

Unintegrable((d*x+c)^m*(a+a*tanh(f*x+e))^2,x)

Rubi [N/A]

Not integrable

Time = 0.03 (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 = {} \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]

[In]

Int[(c + d*x)^m*(a + a*Tanh[e + f*x])^2,x]

[Out]

Defer[Int][(c + d*x)^m*(a + a*Tanh[e + f*x])^2, x]

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

Mathematica [N/A]

Not integrable

Time = 27.84 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]

[In]

Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x])^2,x]

[Out]

Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x])^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.05 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00

\[\int \left (d x +c \right )^{m} \left (a +a \tanh \left (f x +e \right )\right )^{2}d x\]

[In]

int((d*x+c)^m*(a+a*tanh(f*x+e))^2,x)

[Out]

int((d*x+c)^m*(a+a*tanh(f*x+e))^2,x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.85 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m} \,d x } \]

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="fricas")

[Out]

integral((a^2*tanh(f*x + e)^2 + 2*a^2*tanh(f*x + e) + a^2)*(d*x + c)^m, x)

Sympy [N/A]

Not integrable

Time = 2.28 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.20 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=a^{2} \left (\int 2 \left (c + d x\right )^{m} \tanh {\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m} \tanh ^{2}{\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \]

[In]

integrate((d*x+c)**m*(a+a*tanh(f*x+e))**2,x)

[Out]

a**2*(Integral(2*(c + d*x)**m*tanh(e + f*x), x) + Integral((c + d*x)**m*tanh(e + f*x)**2, x) + Integral((c + d
*x)**m, x))

Maxima [N/A]

Not integrable

Time = 0.48 (sec) , antiderivative size = 122, normalized size of antiderivative = 6.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m} \,d x } \]

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="maxima")

[Out]

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

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m} \,d x } \]

[In]

integrate((d*x+c)^m*(a+a*tanh(f*x+e))^2,x, algorithm="giac")

[Out]

integrate((a*tanh(f*x + e) + a)^2*(d*x + c)^m, x)

Mupad [N/A]

Not integrable

Time = 1.96 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int {\left (a+a\,\mathrm {tanh}\left (e+f\,x\right )\right )}^2\,{\left (c+d\,x\right )}^m \,d x \]

[In]

int((a + a*tanh(e + f*x))^2*(c + d*x)^m,x)

[Out]

int((a + a*tanh(e + f*x))^2*(c + d*x)^m, x)