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

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {\cosh \left (a+b x+c x^2\right )}{d+e x},x\right ) \]

[Out]

Unintegrable(cosh(c*x^2+b*x+a)/(e*x+d),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 = {} \[ \int \frac {\cosh \left (a+b x+c x^2\right )}{d+e x} \, dx \]

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*}

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Mathematica [A]  time = 2.61, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (a+b x+c x^2\right )}{d+e x} \, dx \]

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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fricas [A]  time = 0.54, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (c x^{2} + b x + a\right )}{e x + d}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (c x^{2} + b x + a\right )}{e x + d}\,{d x} \]

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)

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maple [A]  time = 0.17, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (c \,x^{2}+b x +a \right )}{e x +d}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (c x^{2} + b x + a\right )}{e x + d}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\mathrm {cosh}\left (c\,x^2+b\,x+a\right )}{d+e\,x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh {\left (a + b x + c x^{2} \right )}}{d + e x}\, dx \]

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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