### 3.30 $$\int \frac{\cosh (a+b x+c x^2)}{d+e x} \, dx$$

Optimal. Leaf size=21 $\text{Unintegrable}\left (\frac{\cosh \left (a+b x+c x^2\right )}{d+e x},x\right )$

[Out]

Unintegrable[Cosh[a + b*x + c*x^2]/(d + e*x), x]

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Rubi [A]  time = 0.0153, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int \frac{\cosh \left (a+b x+c x^2\right )}{d+e x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Cosh[a + b*x + c*x^2]/(d + e*x),x]

[Out]

Defer[Int][Cosh[a + b*x + c*x^2]/(d + e*x), x]

Rubi steps

\begin{align*} \int \frac{\cosh \left (a+b x+c x^2\right )}{d+e x} \, dx &=\int \frac{\cosh \left (a+b x+c x^2\right )}{d+e x} \, dx\\ \end{align*}

Mathematica [A]  time = 2.46225, size = 0, normalized size = 0. $\int \frac{\cosh \left (a+b x+c x^2\right )}{d+e x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Cosh[a + b*x + c*x^2]/(d + e*x),x]

[Out]

Integrate[Cosh[a + b*x + c*x^2]/(d + e*x), x]

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Maple [A]  time = 0.079, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cosh \left ( c{x}^{2}+bx+a \right ) }{ex+d}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh \left (c x^{2} + b x + a\right )}{e x + d}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(c*x^2+b*x+a)/(e*x+d),x, algorithm="maxima")

[Out]

integrate(cosh(c*x^2 + b*x + a)/(e*x + d), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cosh \left (c x^{2} + b x + a\right )}{e x + d}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(c*x^2+b*x+a)/(e*x+d),x, algorithm="fricas")

[Out]

integral(cosh(c*x^2 + b*x + a)/(e*x + d), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh{\left (a + b x + c x^{2} \right )}}{d + e x}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(c*x**2+b*x+a)/(e*x+d),x)

[Out]

Integral(cosh(a + b*x + c*x**2)/(d + e*x), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh \left (c x^{2} + b x + a\right )}{e x + d}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(c*x^2+b*x+a)/(e*x+d),x, algorithm="giac")

[Out]

integrate(cosh(c*x^2 + b*x + a)/(e*x + d), x)