Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\sin \left (a+\frac {b}{(c+d x)^{3/2}}\right )}{e+f x},x\right ) \]
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Rubi [A]
time = 0.01, 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 \frac {\sin \left (a+\frac {b}{(c+d x)^{3/2}}\right )}{e+f x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sin \left (a+\frac {b}{(c+d x)^{3/2}}\right )}{e+f x} \, dx &=\int \frac {\sin \left (a+\frac {b}{(c+d x)^{3/2}}\right )}{e+f x} \, dx\\ \end {align*}
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Mathematica [A]
time = 9.36, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sin \left (a+\frac {b}{(c+d x)^{3/2}}\right )}{e+f x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\sin \left (a +\frac {b}{\left (d x +c \right )^{\frac {3}{2}}}\right )}{f x +e}\, dx\]
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*} \int \frac {\sin {\left (a + \frac {b}{c \sqrt {c + d x} + d x \sqrt {c + d x}} \right )}}{e + f x}\, dx \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 \frac {\sin \left (a+\frac {b}{{\left (c+d\,x\right )}^{3/2}}\right )}{e+f\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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