Optimal. Leaf size=13 \[ e^{\sin (x)} (x \cos (x)-1) \sec (x) \]
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Rubi [F] time = 0.64, 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 = {} \[ \int e^{\sin (x)} \sec ^2(x) \left (x \cos ^3(x)-\sin (x)\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int e^{\sin (x)} \sec ^2(x) \left (x \cos ^3(x)-\sin (x)\right ) \, dx &=\int \left (e^{\sin (x)} x \cos (x)-e^{\sin (x)} \sec (x) \tan (x)\right ) \, dx\\ &=\int e^{\sin (x)} x \cos (x) \, dx-\int e^{\sin (x)} \sec (x) \tan (x) \, dx\\ \end {align*}
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Mathematica [A] time = 0.29, size = 13, normalized size = 1.00 \[ e^{\sin (x)} (x \cos (x)-1) \sec (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 14, normalized size = 1.08 \[ \frac {{\left (x \cos \relax (x) - 1\right )} e^{\sin \relax (x)}}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 794, normalized size = 61.08 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.39, size = 30, normalized size = 2.31 \[ \frac {\left (x \,{\mathrm e}^{2 i x}+x -2 \,{\mathrm e}^{i x}\right ) {\mathrm e}^{\sin \relax (x )}}{{\mathrm e}^{2 i x}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.77, size = 88, normalized size = 6.77 \[ \frac {x \cos \left (2 \, x\right )^{2} e^{\sin \relax (x)} + x e^{\sin \relax (x)} \sin \left (2 \, x\right )^{2} - 2 \, e^{\sin \relax (x)} \sin \left (2 \, x\right ) \sin \relax (x) + 2 \, {\left (x e^{\sin \relax (x)} - \cos \relax (x) e^{\sin \relax (x)}\right )} \cos \left (2 \, x\right ) + x e^{\sin \relax (x)} - 2 \, \cos \relax (x) e^{\sin \relax (x)}}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} + 2 \, \cos \left (2 \, x\right ) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.12, size = 14, normalized size = 1.08 \[ \frac {{\mathrm {e}}^{\sin \relax (x)}\,\left (x\,\cos \relax (x)-1\right )}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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