Optimal. Leaf size=25 \[ \text {Int}\left (\tan (a+b x) \sec ^2(a+b x) (c+d x)^m,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.15, 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 = {} \[ \int (c+d x)^m \sec ^2(a+b x) \tan (a+b x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int (c+d x)^m \sec ^2(a+b x) \tan (a+b x) \, dx &=\int (c+d x)^m \sec ^2(a+b x) \tan (a+b x) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 5.41, size = 0, normalized size = 0.00 \[ \int (c+d x)^m \sec ^2(a+b x) \tan (a+b x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (d x + c\right )}^{m} \sec \left (b x + a\right )^{2} \tan \left (b x + a\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )}^{m} \sec \left (b x + a\right )^{2} \tan \left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 0, normalized size = 0.00 \[ \int \left (d x +c \right )^{m} \left (\sec ^{2}\left (b x +a \right )\right ) \tan \left (b x +a \right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )}^{m} \sec \left (b x + a\right )^{2} \tan \left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\mathrm {tan}\left (a+b\,x\right )\,{\left (c+d\,x\right )}^m}{{\cos \left (a+b\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (c + d x\right )^{m} \tan {\left (a + b x \right )} \sec ^{2}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________