3.171 \(\int \frac {1}{(c+d x) (a+b \cosh (e+f x))} \, dx\)

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x) (a+b \cosh (e+f x))},x\right ) \]

[Out]

Unintegrable(1/(d*x+c)/(a+b*cosh(f*x+e)),x)

________________________________________________________________________________________

Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {1}{(c+d x) (a+b \cosh (e+f x))} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/((c + d*x)*(a + b*Cosh[e + f*x])),x]

[Out]

Defer[Int][1/((c + d*x)*(a + b*Cosh[e + f*x])), x]

Rubi steps

\begin {align*} \int \frac {1}{(c+d x) (a+b \cosh (e+f x))} \, dx &=\int \frac {1}{(c+d x) (a+b \cosh (e+f x))} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.97, size = 0, normalized size = 0.00 \[ \int \frac {1}{(c+d x) (a+b \cosh (e+f x))} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/((c + d*x)*(a + b*Cosh[e + f*x])),x]

[Out]

Integrate[1/((c + d*x)*(a + b*Cosh[e + f*x])), x]

________________________________________________________________________________________

fricas [A]  time = 1.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a d x + a c + {\left (b d x + b c\right )} \cosh \left (f x + e\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)/(a+b*cosh(f*x+e)),x, algorithm="fricas")

[Out]

integral(1/(a*d*x + a*c + (b*d*x + b*c)*cosh(f*x + e)), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (d x + c\right )} {\left (b \cosh \left (f x + e\right ) + a\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)/(a+b*cosh(f*x+e)),x, algorithm="giac")

[Out]

integrate(1/((d*x + c)*(b*cosh(f*x + e) + a)), x)

________________________________________________________________________________________

maple [A]  time = 0.17, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d x +c \right ) \left (a +b \cosh \left (f x +e \right )\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(d*x+c)/(a+b*cosh(f*x+e)),x)

[Out]

int(1/(d*x+c)/(a+b*cosh(f*x+e)),x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (d x + c\right )} {\left (b \cosh \left (f x + e\right ) + a\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)/(a+b*cosh(f*x+e)),x, algorithm="maxima")

[Out]

integrate(1/((d*x + c)*(b*cosh(f*x + e) + a)), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{\left (a+b\,\mathrm {cosh}\left (e+f\,x\right )\right )\,\left (c+d\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((a + b*cosh(e + f*x))*(c + d*x)),x)

[Out]

int(1/((a + b*cosh(e + f*x))*(c + d*x)), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a + b \cosh {\left (e + f x \right )}\right ) \left (c + d x\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)/(a+b*cosh(f*x+e)),x)

[Out]

Integral(1/((a + b*cosh(e + f*x))*(c + d*x)), x)

________________________________________________________________________________________