Integrand size = 18, antiderivative size = 18 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\text {Int}\left (\frac {x^4}{a+b \csc \left (c+d x^2\right )},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx \\ \end{align*}
Not integrable
Time = 2.41 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx \]
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Not integrable
Time = 0.14 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {x^{4}}{a +b \csc \left (d \,x^{2}+c \right )}d x\]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int { \frac {x^{4}}{b \csc \left (d x^{2} + c\right ) + a} \,d x } \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int \frac {x^{4}}{a + b \csc {\left (c + d x^{2} \right )}}\, dx \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 253, normalized size of antiderivative = 14.06 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int { \frac {x^{4}}{b \csc \left (d x^{2} + c\right ) + a} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int { \frac {x^{4}}{b \csc \left (d x^{2} + c\right ) + a} \,d x } \]
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Not integrable
Time = 18.15 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {x^4}{a+b \csc \left (c+d x^2\right )} \, dx=\int \frac {x^4}{a+\frac {b}{\sin \left (d\,x^2+c\right )}} \,d x \]
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