Integrand size = 16, antiderivative size = 8 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \arccos (x)^2} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {4738} \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \arccos (x)^2} \]
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Rule 4738
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2 \arccos (x)^2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \arccos (x)^2} \]
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Time = 0.17 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88
method | result | size |
derivativedivides | \(\frac {1}{2 \arccos \left (x \right )^{2}}\) | \(7\) |
default | \(\frac {1}{2 \arccos \left (x \right )^{2}}\) | \(7\) |
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none
Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \, \arccos \left (x\right )^{2}} \]
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Time = 0.41 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \operatorname {acos}^{2}{\left (x \right )}} \]
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none
Time = 0.31 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \, \arccos \left (x\right )^{2}} \]
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2 \, \arccos \left (x\right )^{2}} \]
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Time = 0.39 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \frac {1}{\sqrt {1-x^2} \arccos (x)^3} \, dx=\frac {1}{2\,{\mathrm {acos}\left (x\right )}^2} \]
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