\(\int x^m \tanh (a+b x) \, dx\) [31]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int x^m \tanh (a+b x) \, dx=\text {Int}\left (x^m \tanh (a+b x),x\right ) \]

[Out]

Unintegrable(x^m*tanh(b*x+a),x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int x^m \tanh (a+b x) \, dx=\int x^m \tanh (a+b x) \, dx \]

[In]

Int[x^m*Tanh[a + b*x],x]

[Out]

Defer[Int][x^m*Tanh[a + b*x], x]

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

Mathematica [N/A]

Not integrable

Time = 6.18 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \tanh (a+b x) \, dx=\int x^m \tanh (a+b x) \, dx \]

[In]

Integrate[x^m*Tanh[a + b*x],x]

[Out]

Integrate[x^m*Tanh[a + b*x], x]

Maple [N/A] (verified)

Not integrable

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int x^{m} \tanh \left (b x +a \right )d x\]

[In]

int(x^m*tanh(b*x+a),x)

[Out]

int(x^m*tanh(b*x+a),x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \tanh (a+b x) \, dx=\int { x^{m} \tanh \left (b x + a\right ) \,d x } \]

[In]

integrate(x^m*tanh(b*x+a),x, algorithm="fricas")

[Out]

integral(x^m*tanh(b*x + a), x)

Sympy [N/A]

Not integrable

Time = 0.42 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x^m \tanh (a+b x) \, dx=\int x^{m} \tanh {\left (a + b x \right )}\, dx \]

[In]

integrate(x**m*tanh(b*x+a),x)

[Out]

Integral(x**m*tanh(a + b*x), x)

Maxima [N/A]

Not integrable

Time = 0.46 (sec) , antiderivative size = 100, normalized size of antiderivative = 10.00 \[ \int x^m \tanh (a+b x) \, dx=\int { x^{m} \tanh \left (b x + a\right ) \,d x } \]

[In]

integrate(x^m*tanh(b*x+a),x, algorithm="maxima")

[Out]

x*e^(2*b*x + m*log(x) + 2*a)/((m + 1)*e^(2*b*x + 2*a) + m + 1) - integrate(((2*b*x*e^(2*a) + (m + 1)*e^(2*a))*
e^(2*b*x) + m + 1)*x^m/((m + 1)*e^(4*b*x + 4*a) + 2*(m + 1)*e^(2*b*x + 2*a) + m + 1), x)

Giac [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \tanh (a+b x) \, dx=\int { x^{m} \tanh \left (b x + a\right ) \,d x } \]

[In]

integrate(x^m*tanh(b*x+a),x, algorithm="giac")

[Out]

integrate(x^m*tanh(b*x + a), x)

Mupad [N/A]

Not integrable

Time = 1.70 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \tanh (a+b x) \, dx=\int x^m\,\mathrm {tanh}\left (a+b\,x\right ) \,d x \]

[In]

int(x^m*tanh(a + b*x),x)

[Out]

int(x^m*tanh(a + b*x), x)