\(\int \frac {\cot (a+b x)}{x} \, dx\) [4]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {\cot (a+b x)}{x} \, dx=\text {Int}\left (\frac {\cot (a+b x)}{x},x\right ) \]

[Out]

Unintegrable(cot(b*x+a)/x,x)

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\cot (a+b x)}{x} \, dx=\int \frac {\cot (a+b x)}{x} \, dx \]

[In]

Int[Cot[a + b*x]/x,x]

[Out]

Defer[Int][Cot[a + b*x]/x, x]

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

Mathematica [N/A]

Not integrable

Time = 2.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\cot (a+b x)}{x} \, dx=\int \frac {\cot (a+b x)}{x} \, dx \]

[In]

Integrate[Cot[a + b*x]/x,x]

[Out]

Integrate[Cot[a + b*x]/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.14 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

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

[In]

int(cot(b*x+a)/x,x)

[Out]

int(cot(b*x+a)/x,x)

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\cot (a+b x)}{x} \, dx=\int { \frac {\cot \left (b x + a\right )}{x} \,d x } \]

[In]

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

[Out]

integral(cot(b*x + a)/x, x)

Sympy [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {\cot (a+b x)}{x} \, dx=\int \frac {\cot {\left (a + b x \right )}}{x}\, dx \]

[In]

integrate(cot(b*x+a)/x,x)

[Out]

Integral(cot(a + b*x)/x, x)

Maxima [N/A]

Not integrable

Time = 0.43 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\cot (a+b x)}{x} \, dx=\int { \frac {\cot \left (b x + a\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(cot(b*x + a)/x, x)

Giac [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\cot (a+b x)}{x} \, dx=\int { \frac {\cot \left (b x + a\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(cot(b*x + a)/x, x)

Mupad [N/A]

Not integrable

Time = 12.14 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\cot (a+b x)}{x} \, dx=\int \frac {\mathrm {cot}\left (a+b\,x\right )}{x} \,d x \]

[In]

int(cot(a + b*x)/x,x)

[Out]

int(cot(a + b*x)/x, x)