3.4.34 \(\int x^m \tanh (a+b x) \, dx\) [334]

Optimal. Leaf size=13 \[ \text {Int}\left (x^m \tanh (a+b x),x\right ) \]

[Out]

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

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Rubi [A]
time = 0.01, 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 = {} \begin {gather*} \int x^m \tanh (a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^m*Tanh[a + b*x],x]

[Out]

Defer[Int][x^m*Tanh[a + b*x], x]

Rubi steps

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

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Mathematica [A]
time = 0.33, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \tanh (a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^m*Tanh[a + b*x],x]

[Out]

Integrate[x^m*Tanh[a + b*x], x]

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Maple [A]
time = 0.19, size = 0, normalized size = 0.00 \[\int x^{m} \mathrm {sech}\left (b x +a \right ) \sinh \left (b x +a \right )\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*sech(b*x+a)*sinh(b*x+a),x)

[Out]

int(x^m*sech(b*x+a)*sinh(b*x+a),x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sech(b*x+a)*sinh(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)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x^m*sech(b*x + a)*sinh(b*x + a), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{m} \sinh {\left (a + b x \right )} \operatorname {sech}{\left (a + b x \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*sech(b*x+a)*sinh(b*x+a),x)

[Out]

Integral(x**m*sinh(a + b*x)*sech(a + b*x), x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*sech(b*x + a)*sinh(b*x + a), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {x^m\,\mathrm {sinh}\left (a+b\,x\right )}{\mathrm {cosh}\left (a+b\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^m*sinh(a + b*x))/cosh(a + b*x),x)

[Out]

int((x^m*sinh(a + b*x))/cosh(a + b*x), x)

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