3.39 \(\int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx\)

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {sech}^3(a+b x)}{c+d x},x\right ) \]

[Out]

Unintegrable(sech(b*x+a)^3/(d*x+c),x)

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sech[a + b*x]^3/(c + d*x),x]

[Out]

Defer[Int][Sech[a + b*x]^3/(c + d*x), x]

Rubi steps

\begin {align*} \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx &=\int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx\\ \end {align*}

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Mathematica [F]  time = 180.01, size = 0, normalized size = 0.00 \[ \text {\$Aborted} \]

Verification is Not applicable to the result.

[In]

Integrate[Sech[a + b*x]^3/(c + d*x),x]

[Out]

$Aborted

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fricas [A]  time = 0.86, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)^3/(d*x+c),x, algorithm="fricas")

[Out]

integral(sech(b*x + a)^3/(d*x + c), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)^3/(d*x+c),x, algorithm="giac")

[Out]

integrate(sech(b*x + a)^3/(d*x + c), x)

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maple [A]  time = 0.52, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {sech}\left (b x +a \right )^{3}}{d x +c}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sech(b*x+a)^3/(d*x+c),x)

[Out]

int(sech(b*x+a)^3/(d*x+c),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {{\left (b d x e^{\left (3 \, a\right )} + {\left (b c - d\right )} e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} - {\left (b d x e^{a} + {\left (b c + d\right )} e^{a}\right )} e^{\left (b x\right )}}{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + {\left (b^{2} d^{2} x^{2} e^{\left (4 \, a\right )} + 2 \, b^{2} c d x e^{\left (4 \, a\right )} + b^{2} c^{2} e^{\left (4 \, a\right )}\right )} e^{\left (4 \, b x\right )} + 2 \, {\left (b^{2} d^{2} x^{2} e^{\left (2 \, a\right )} + 2 \, b^{2} c d x e^{\left (2 \, a\right )} + b^{2} c^{2} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} + 8 \, \int \frac {{\left (b^{2} d^{2} x^{2} e^{a} + 2 \, b^{2} c d x e^{a} + {\left (b^{2} c^{2} - 2 \, d^{2}\right )} e^{a}\right )} e^{\left (b x\right )}}{8 \, {\left (b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left (b^{2} d^{3} x^{3} e^{\left (2 \, a\right )} + 3 \, b^{2} c d^{2} x^{2} e^{\left (2 \, a\right )} + 3 \, b^{2} c^{2} d x e^{\left (2 \, a\right )} + b^{2} c^{3} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)^3/(d*x+c),x, algorithm="maxima")

[Out]

((b*d*x*e^(3*a) + (b*c - d)*e^(3*a))*e^(3*b*x) - (b*d*x*e^a + (b*c + d)*e^a)*e^(b*x))/(b^2*d^2*x^2 + 2*b^2*c*d
*x + b^2*c^2 + (b^2*d^2*x^2*e^(4*a) + 2*b^2*c*d*x*e^(4*a) + b^2*c^2*e^(4*a))*e^(4*b*x) + 2*(b^2*d^2*x^2*e^(2*a
) + 2*b^2*c*d*x*e^(2*a) + b^2*c^2*e^(2*a))*e^(2*b*x)) + 8*integrate(1/8*(b^2*d^2*x^2*e^a + 2*b^2*c*d*x*e^a + (
b^2*c^2 - 2*d^2)*e^a)*e^(b*x)/(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3*e^(2*a)
+ 3*b^2*c*d^2*x^2*e^(2*a) + 3*b^2*c^2*d*x*e^(2*a) + b^2*c^3*e^(2*a))*e^(2*b*x)), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{{\mathrm {cosh}\left (a+b\,x\right )}^3\,\left (c+d\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(cosh(a + b*x)^3*(c + d*x)),x)

[Out]

int(1/(cosh(a + b*x)^3*(c + d*x)), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {sech}^{3}{\left (a + b x \right )}}{c + d x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)**3/(d*x+c),x)

[Out]

Integral(sech(a + b*x)**3/(c + d*x), x)

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