3.1.69 \(\int \frac {\text {sech}(a+b x)}{\sqrt {c+d x}} \, dx\) [69]

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

[Out]

Unintegrable(sech(b*x+a)/(d*x+c)^(1/2),x)

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Rubi [A]
time = 0.02, 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 \frac {\text {sech}(a+b x)}{\sqrt {c+d x}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sech[a + b*x]/Sqrt[c + d*x],x]

[Out]

Defer[Int][Sech[a + b*x]/Sqrt[c + d*x], x]

Rubi steps

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

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Mathematica [A]
time = 8.18, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {sech}(a+b x)}{\sqrt {c+d x}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sech[a + b*x]/Sqrt[c + d*x],x]

[Out]

Integrate[Sech[a + b*x]/Sqrt[c + d*x], x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sech(b*x+a)/(d*x+c)^(1/2),x)

[Out]

int(sech(b*x+a)/(d*x+c)^(1/2),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(sech(b*x+a)/(d*x+c)^(1/2),x, algorithm="maxima")

[Out]

integrate(sech(b*x + a)/sqrt(d*x + c), 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(sech(b*x+a)/(d*x+c)^(1/2),x, algorithm="fricas")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)/(d*x+c)**(1/2),x)

[Out]

Integral(sech(a + b*x)/sqrt(c + d*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(sech(b*x+a)/(d*x+c)^(1/2),x, algorithm="giac")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(cosh(a + b*x)*(c + d*x)^(1/2)),x)

[Out]

int(1/(cosh(a + b*x)*(c + d*x)^(1/2)), x)

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