\(\int \frac {\sinh (a+b x-c x^2)}{x} \, dx\) [9]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\text {Int}\left (\frac {\sinh \left (a+b x-c x^2\right )}{x},x\right ) \]

[Out]

Unintegrable(sinh(-c*x^2+b*x+a)/x,x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx \]

[In]

Int[Sinh[a + b*x - c*x^2]/x,x]

[Out]

Defer[Int][Sinh[a + b*x - c*x^2]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 6.64 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx \]

[In]

Integrate[Sinh[a + b*x - c*x^2]/x,x]

[Out]

Integrate[Sinh[a + b*x - c*x^2]/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.29 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

\[\int \frac {\sinh \left (-c \,x^{2}+b x +a \right )}{x}d x\]

[In]

int(sinh(-c*x^2+b*x+a)/x,x)

[Out]

int(sinh(-c*x^2+b*x+a)/x,x)

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.31 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int { \frac {\sinh \left (-c x^{2} + b x + a\right )}{x} \,d x } \]

[In]

integrate(sinh(-c*x^2+b*x+a)/x,x, algorithm="fricas")

[Out]

integral(-sinh(c*x^2 - b*x - a)/x, x)

Sympy [N/A]

Not integrable

Time = 0.60 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int \frac {\sinh {\left (a + b x - c x^{2} \right )}}{x}\, dx \]

[In]

integrate(sinh(-c*x**2+b*x+a)/x,x)

[Out]

Integral(sinh(a + b*x - c*x**2)/x, x)

Maxima [N/A]

Not integrable

Time = 0.72 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int { \frac {\sinh \left (-c x^{2} + b x + a\right )}{x} \,d x } \]

[In]

integrate(sinh(-c*x^2+b*x+a)/x,x, algorithm="maxima")

[Out]

-integrate(sinh(c*x^2 - b*x - a)/x, x)

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int { \frac {\sinh \left (-c x^{2} + b x + a\right )}{x} \,d x } \]

[In]

integrate(sinh(-c*x^2+b*x+a)/x,x, algorithm="giac")

[Out]

integrate(sinh(-c*x^2 + b*x + a)/x, x)

Mupad [N/A]

Not integrable

Time = 1.12 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sinh \left (a+b x-c x^2\right )}{x} \, dx=\int \frac {\mathrm {sinh}\left (-c\,x^2+b\,x+a\right )}{x} \,d x \]

[In]

int(sinh(a + b*x - c*x^2)/x,x)

[Out]

int(sinh(a + b*x - c*x^2)/x, x)