\(\int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx\) [150]

Optimal result

Integrand size = 21, antiderivative size = 21 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\text {Int}\left (\frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x},x\right ) \]

[Out]

Unintegrable((a+I*a*sinh(f*x+e))^(1/3)/x,x)

Rubi [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 21, 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 = {} \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx \]

[In]

Int[(a + I*a*Sinh[e + f*x])^(1/3)/x,x]

[Out]

Defer[Int][(a + I*a*Sinh[e + f*x])^(1/3)/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 4.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx \]

[In]

Integrate[(a + I*a*Sinh[e + f*x])^(1/3)/x,x]

[Out]

Integrate[(a + I*a*Sinh[e + f*x])^(1/3)/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.17 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81

\[\int \frac {\left (a +i a \sinh \left (f x +e \right )\right )^{\frac {1}{3}}}{x}d x\]

[In]

int((a+I*a*sinh(f*x+e))^(1/3)/x,x)

[Out]

int((a+I*a*sinh(f*x+e))^(1/3)/x,x)

Fricas [F(-2)]

Exception generated. \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (ha
s polynomial part)

Sympy [N/A]

Not integrable

Time = 2.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\int \frac {\sqrt [3]{i a \left (\sinh {\left (e + f x \right )} - i\right )}}{x}\, dx \]

[In]

integrate((a+I*a*sinh(f*x+e))**(1/3)/x,x)

[Out]

Integral((I*a*(sinh(e + f*x) - I))**(1/3)/x, x)

Maxima [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\int { \frac {{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{\frac {1}{3}}}{x} \,d x } \]

[In]

integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm="maxima")

[Out]

integrate((I*a*sinh(f*x + e) + a)^(1/3)/x, x)

Giac [N/A]

Not integrable

Time = 0.36 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\int { \frac {{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{\frac {1}{3}}}{x} \,d x } \]

[In]

integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm="giac")

[Out]

integrate((I*a*sinh(f*x + e) + a)^(1/3)/x, x)

Mupad [N/A]

Not integrable

Time = 0.91 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx=\int \frac {{\left (a+a\,\mathrm {sinh}\left (e+f\,x\right )\,1{}\mathrm {i}\right )}^{1/3}}{x} \,d x \]

[In]

int((a + a*sinh(e + f*x)*1i)^(1/3)/x,x)

[Out]

int((a + a*sinh(e + f*x)*1i)^(1/3)/x, x)