Optimal. Leaf size=21 \[ \text {Int}\left (\frac {a \sec (e+f x)+a}{(c+d x)^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {a+a \sec (e+f x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {a+a \sec (e+f x)}{(c+d x)^2} \, dx &=\int \frac {a+a \sec (e+f x)}{(c+d x)^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 6.47, size = 0, normalized size = 0.00 \[ \int \frac {a+a \sec (e+f x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.77, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {a \sec \left (f x + e\right ) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {a \sec \left (f x + e\right ) + a}{{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 1.23, size = 0, normalized size = 0.00 \[ \int \frac {a +a \sec \left (f x +e \right )}{\left (d x +c \right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {a+\frac {a}{\cos \left (e+f\,x\right )}}{{\left (c+d\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ a \left (\int \frac {\sec {\left (e + f x \right )}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac {1}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________