Integrand size = 18, antiderivative size = 18 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=a \log (x)+b \text {Int}\left (\frac {\tan \left (c+d \sqrt {x}\right )}{x},x\right ) \]
[Out]
Not integrable
Time = 0.02 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x}+\frac {b \tan \left (c+d \sqrt {x}\right )}{x}\right ) \, dx \\ & = a \log (x)+b \int \frac {\tan \left (c+d \sqrt {x}\right )}{x} \, dx \\ \end{align*}
Not integrable
Time = 5.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.45 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89
\[\int \frac {a +b \tan \left (c +d \sqrt {x}\right )}{x}d x\]
[In]
[Out]
Not integrable
Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int { \frac {b \tan \left (d \sqrt {x} + c\right ) + a}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.55 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int \frac {a + b \tan {\left (c + d \sqrt {x} \right )}}{x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.53 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.78 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int { \frac {b \tan \left (d \sqrt {x} + c\right ) + a}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.48 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int { \frac {b \tan \left (d \sqrt {x} + c\right ) + a}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 4.05 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {a+b \tan \left (c+d \sqrt {x}\right )}{x} \, dx=\int \frac {a+b\,\mathrm {tan}\left (c+d\,\sqrt {x}\right )}{x} \,d x \]
[In]
[Out]