Integrand size = 10, antiderivative size = 10 \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=-\frac {\cos ^{\frac {3}{2}}(x)}{2 x^2}+\frac {3 \sqrt {\cos (x)} \sin (x)}{4 x}+\frac {3}{8} \text {Int}\left (\frac {1}{x \sqrt {\cos (x)}},x\right )-\frac {9}{8} \text {Int}\left (\frac {\cos ^{\frac {3}{2}}(x)}{x},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\frac {\cos ^{\frac {3}{2}}(x)}{2 x^2}+\frac {3 \sqrt {\cos (x)} \sin (x)}{4 x}+\frac {3}{8} \int \frac {1}{x \sqrt {\cos (x)}} \, dx-\frac {9}{8} \int \frac {\cos ^{\frac {3}{2}}(x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 6.11 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx \]
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Not integrable
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80
\[\int \frac {\cos ^{\frac {3}{2}}\left (x \right )}{x^{3}}d x\]
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Exception generated. \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 92.97 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\int \frac {\cos ^{\frac {3}{2}}{\left (x \right )}}{x^{3}}\, dx \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\int { \frac {\cos \left (x\right )^{\frac {3}{2}}}{x^{3}} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\int { \frac {\cos \left (x\right )^{\frac {3}{2}}}{x^{3}} \,d x } \]
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Not integrable
Time = 13.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx=\int \frac {{\cos \left (x\right )}^{3/2}}{x^3} \,d x \]
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