Optimal. Leaf size=26 \[ \text {Int}\left ((c+d x)^m (a+i a \tan (e+f x))^2,x\right ) \]
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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 = {}
\begin {gather*} \int (c+d x)^m (a+i a \tan (e+f x))^2 \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int (c+d x)^m (a+i a \tan (e+f x))^2 \, dx &=\int (c+d x)^m (a+i a \tan (e+f x))^2 \, dx\\ \end {align*}
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Mathematica [A]
time = 30.54, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^m (a+i a \tan (e+f x))^2 \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.20, size = 0, normalized size = 0.00 \[\int \left (d x +c \right )^{m} \left (a +i a \tan \left (f x +e \right )\right )^{2}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - a^{2} \left (\int \left (c + d x\right )^{m} \tan ^{2}{\left (e + f x \right )}\, dx + \int \left (- 2 i \left (c + d x\right )^{m} \tan {\left (e + f x \right )}\right )\, dx + \int \left (- \left (c + d x\right )^{m}\right )\, dx\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int {\left (a+a\,\mathrm {tan}\left (e+f\,x\right )\,1{}\mathrm {i}\right )}^2\,{\left (c+d\,x\right )}^m \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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