\(\int \frac {\sinh ((a+b x)^2)}{x} \, dx\) [91]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=b \text {Int}\left (\frac {\sinh \left ((a+b x)^2\right )}{b x},x\right ) \]

[Out]

b*CannotIntegrate(sinh((b*x+a)^2)/b/x,x)

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx \]

[In]

Int[Sinh[(a + b*x)^2]/x,x]

[Out]

Defer[Subst][Defer[Int][Sinh[x^2]/(-a + x), x], x, a + b*x]

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

Mathematica [N/A]

Not integrable

Time = 5.13 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx \]

[In]

Integrate[Sinh[(a + b*x)^2]/x,x]

[Out]

Integrate[Sinh[(a + b*x)^2]/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int { \frac {\sinh \left ({\left (b x + a\right )}^{2}\right )}{x} \,d x } \]

[In]

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

[Out]

integral(sinh(b^2*x^2 + 2*a*b*x + a^2)/x, x)

Sympy [N/A]

Not integrable

Time = 2.55 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\sinh {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x}\, dx \]

[In]

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

[Out]

Integral(sinh(a**2 + 2*a*b*x + b**2*x**2)/x, x)

Maxima [N/A]

Not integrable

Time = 0.85 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int { \frac {\sinh \left ({\left (b x + a\right )}^{2}\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(sinh((b*x + a)^2)/x, x)

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int { \frac {\sinh \left ({\left (b x + a\right )}^{2}\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(sinh((b*x + a)^2)/x, x)

Mupad [N/A]

Not integrable

Time = 1.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\sinh \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\mathrm {sinh}\left ({\left (a+b\,x\right )}^2\right )}{x} \,d x \]

[In]

int(sinh((a + b*x)^2)/x,x)

[Out]

int(sinh((a + b*x)^2)/x, x)