Optimal. Leaf size=28 \[ \text {Int}\left (\frac {1}{\sec ^{\frac {7}{3}}(c+d x) \sqrt {a+b \sec (c+d x)}},x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int \frac {1}{\sec ^{\frac {7}{3}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\sec ^{\frac {7}{3}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx &=\int \frac {1}{\sec ^{\frac {7}{3}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx\\ \end {align*}
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Mathematica [A] time = 41.79, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sec ^{\frac {7}{3}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 2.08, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {b \sec \left (d x + c\right ) + a} \sec \left (d x + c\right )^{\frac {2}{3}}}{b \sec \left (d x + c\right )^{4} + a \sec \left (d x + c\right )^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [A] time = 1.56, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sec \left (d x +c \right )^{\frac {7}{3}} \sqrt {a +b \sec \left (d x +c \right )}}\, dx \]
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 \[ \int \frac {1}{\sqrt {b \sec \left (d x + c\right ) + a} \sec \left (d x + c\right )^{\frac {7}{3}}}\,{d x} \]
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 \[ \int \frac {1}{\sqrt {a+\frac {b}{\cos \left (c+d\,x\right )}}\,{\left (\frac {1}{\cos \left (c+d\,x\right )}\right )}^{7/3}} \,d x \]
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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