\(\int \frac {\tan (a+b x)}{x^2} \, dx\) [5]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\text {Int}\left (\frac {\tan (a+b x)}{x^2},x\right ) \]

[Out]

Unintegrable(tan(b*x+a)/x^2,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 = {} \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int \frac {\tan (a+b x)}{x^2} \, dx \]

[In]

Int[Tan[a + b*x]/x^2,x]

[Out]

Defer[Int][Tan[a + b*x]/x^2, x]

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

Mathematica [N/A]

Not integrable

Time = 2.42 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int \frac {\tan (a+b x)}{x^2} \, dx \]

[In]

Integrate[Tan[a + b*x]/x^2,x]

[Out]

Integrate[Tan[a + b*x]/x^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int { \frac {\tan \left (b x + a\right )}{x^{2}} \,d x } \]

[In]

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

[Out]

integral(tan(b*x + a)/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int \frac {\tan {\left (a + b x \right )}}{x^{2}}\, dx \]

[In]

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

[Out]

Integral(tan(a + b*x)/x**2, x)

Maxima [N/A]

Not integrable

Time = 0.45 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int { \frac {\tan \left (b x + a\right )}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(tan(b*x + a)/x^2, x)

Giac [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int { \frac {\tan \left (b x + a\right )}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(tan(b*x + a)/x^2, x)

Mupad [N/A]

Not integrable

Time = 3.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x^2} \, dx=\int \frac {\mathrm {tan}\left (a+b\,x\right )}{x^2} \,d x \]

[In]

int(tan(a + b*x)/x^2,x)

[Out]

int(tan(a + b*x)/x^2, x)