3.1.80 \(\int (c+d x)^m \text {sech}^2(a+b x) \, dx\) [80]

Optimal. Leaf size=19 \[ \text {Int}\left ((c+d x)^m \text {sech}^2(a+b x),x\right ) \]

[Out]

Unintegrable((d*x+c)^m*sech(b*x+a)^2,x)

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Rubi [A]
time = 0.03, 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 (c+d x)^m \text {sech}^2(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(c + d*x)^m*Sech[a + b*x]^2,x]

[Out]

Defer[Int][(c + d*x)^m*Sech[a + b*x]^2, x]

Rubi steps

\begin {align*} \int (c+d x)^m \text {sech}^2(a+b x) \, dx &=\int (c+d x)^m \text {sech}^2(a+b x) \, dx\\ \end {align*}

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Mathematica [A]
time = 2.43, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^m \text {sech}^2(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(c + d*x)^m*Sech[a + b*x]^2,x]

[Out]

Integrate[(c + d*x)^m*Sech[a + b*x]^2, x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \left (d x +c \right )^{m} \mathrm {sech}\left (b x +a \right )^{2}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^m*sech(b*x+a)^2,x)

[Out]

int((d*x+c)^m*sech(b*x+a)^2,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((d*x+c)^m*sech(b*x+a)^2,x, algorithm="maxima")

[Out]

integrate((d*x + c)^m*sech(b*x + a)^2, 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((d*x+c)^m*sech(b*x+a)^2,x, algorithm="fricas")

[Out]

integral((d*x + c)^m*sech(b*x + a)^2, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (c + d x\right )^{m} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**m*sech(b*x+a)**2,x)

[Out]

Integral((c + d*x)**m*sech(a + b*x)**2, 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((d*x+c)^m*sech(b*x+a)^2,x, algorithm="giac")

[Out]

integrate((d*x + c)^m*sech(b*x + a)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\left (c+d\,x\right )}^m}{{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^m/cosh(a + b*x)^2,x)

[Out]

int((c + d*x)^m/cosh(a + b*x)^2, x)

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