Optimal. Leaf size=16 \[ b \text{Unintegrable}\left (\tan \left (c+d x^2\right ),x\right )+a x \]
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Rubi [A] time = 0.0045918, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \left (a+b \tan \left (c+d x^2\right )\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \left (a+b \tan \left (c+d x^2\right )\right ) \, dx &=a x+b \int \tan \left (c+d x^2\right ) \, dx\\ \end{align*}
Mathematica [A] time = 0.705486, size = 0, normalized size = 0. \[ \int \left (a+b \tan \left (c+d x^2\right )\right ) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.069, size = 0, normalized size = 0. \begin{align*} \int a+b\tan \left ( d{x}^{2}+c \right ) \, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} a x + 2 \, b \int \frac{\sin \left (2 \, d x^{2} + 2 \, c\right )}{\cos \left (2 \, d x^{2} + 2 \, c\right )^{2} + \sin \left (2 \, d x^{2} + 2 \, c\right )^{2} + 2 \, \cos \left (2 \, d x^{2} + 2 \, c\right ) + 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (b \tan \left (d x^{2} + c\right ) + a, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (a + b \tan{\left (c + d x^{2} \right )}\right )\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int b \tan \left (d x^{2} + c\right ) + a\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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