\(\int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx\) [130]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\text {Int}\left (\frac {\cosh (a+b x) \text {Chi}(a+b x)}{x},x\right ) \]

[Out]

CannotIntegrate(Chi(b*x+a)*cosh(b*x+a)/x,x)

Rubi [N/A]

Not integrable

Time = 0.06 (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 = {} \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx \]

[In]

Int[(Cosh[a + b*x]*CoshIntegral[a + b*x])/x,x]

[Out]

Defer[Int][(Cosh[a + b*x]*CoshIntegral[a + b*x])/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.38 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx \]

[In]

Integrate[(Cosh[a + b*x]*CoshIntegral[a + b*x])/x,x]

[Out]

Integrate[(Cosh[a + b*x]*CoshIntegral[a + b*x])/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

\[\int \frac {\operatorname {Chi}\left (b x +a \right ) \cosh \left (b x +a \right )}{x}d x\]

[In]

int(Chi(b*x+a)*cosh(b*x+a)/x,x)

[Out]

int(Chi(b*x+a)*cosh(b*x+a)/x,x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int { \frac {{\rm Chi}\left (b x + a\right ) \cosh \left (b x + a\right )}{x} \,d x } \]

[In]

integrate(Chi(b*x+a)*cosh(b*x+a)/x,x, algorithm="fricas")

[Out]

integral(cosh(b*x + a)*cosh_integral(b*x + a)/x, x)

Sympy [N/A]

Not integrable

Time = 1.12 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int \frac {\cosh {\left (a + b x \right )} \operatorname {Chi}\left (a + b x\right )}{x}\, dx \]

[In]

integrate(Chi(b*x+a)*cosh(b*x+a)/x,x)

[Out]

Integral(cosh(a + b*x)*Chi(a + b*x)/x, x)

Maxima [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int { \frac {{\rm Chi}\left (b x + a\right ) \cosh \left (b x + a\right )}{x} \,d x } \]

[In]

integrate(Chi(b*x+a)*cosh(b*x+a)/x,x, algorithm="maxima")

[Out]

integrate(Chi(b*x + a)*cosh(b*x + a)/x, x)

Giac [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int { \frac {{\rm Chi}\left (b x + a\right ) \cosh \left (b x + a\right )}{x} \,d x } \]

[In]

integrate(Chi(b*x+a)*cosh(b*x+a)/x,x, algorithm="giac")

[Out]

integrate(Chi(b*x + a)*cosh(b*x + a)/x, x)

Mupad [N/A]

Not integrable

Time = 5.15 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cosh (a+b x) \text {Chi}(a+b x)}{x} \, dx=\int \frac {\mathrm {coshint}\left (a+b\,x\right )\,\mathrm {cosh}\left (a+b\,x\right )}{x} \,d x \]

[In]

int((coshint(a + b*x)*cosh(a + b*x))/x,x)

[Out]

int((coshint(a + b*x)*cosh(a + b*x))/x, x)