3.3.93 \(\int \frac {\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\) [293]

Optimal. Leaf size=29 \[ \text {Int}\left (\frac {\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]

[Out]

Unintegrable(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),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 \frac {\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]

[Out]

Defer[Int][Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]

Rubi steps

\begin {align*} \int \frac {\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac {\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end {align*}

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Mathematica [A]
time = 8.76, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]

[Out]

Integrate[Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x)

[Out]

int(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),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(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm="maxima")

[Out]

log(f*x + e)/(b*f) - 1/2*integrate(-4*(a*e^(d*x + c) - b)/(b^2*f*x + b^2*e - (b^2*f*x*e^(2*c) + b^2*e^(2*c + 1
))*e^(2*d*x) - 2*(a*b*f*x*e^c + a*b*e^(c + 1))*e^(d*x)), 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(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm="fricas")

[Out]

integral(cosh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x)

[Out]

Integral(cosh(c + d*x)/((a + b*sinh(c + d*x))*(e + f*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(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm="giac")

[Out]

integrate(cosh(d*x + c)/((f*x + e)*(b*sinh(d*x + c) + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\mathrm {cosh}\left (c+d\,x\right )}{\left (e+f\,x\right )\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(c + d*x)/((e + f*x)*(a + b*sinh(c + d*x))),x)

[Out]

int(cosh(c + d*x)/((e + f*x)*(a + b*sinh(c + d*x))), x)

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