Integrand size = 2, antiderivative size = 16 \[ \int \arcsin (x) \, dx=\sqrt {1-x^2}+x \arcsin (x) \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {4715, 267} \[ \int \arcsin (x) \, dx=x \arcsin (x)+\sqrt {1-x^2} \]
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Rule 267
Rule 4715
Rubi steps \begin{align*} \text {integral}& = x \arcsin (x)-\int \frac {x}{\sqrt {1-x^2}} \, dx \\ & = \sqrt {1-x^2}+x \arcsin (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \arcsin (x) \, dx=\sqrt {1-x^2}+x \arcsin (x) \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
method | result | size |
lookup | \(\arcsin \left (x \right ) x +\sqrt {-x^{2}+1}\) | \(15\) |
default | \(\arcsin \left (x \right ) x +\sqrt {-x^{2}+1}\) | \(15\) |
parts | \(\arcsin \left (x \right ) x +\sqrt {-x^{2}+1}\) | \(15\) |
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none
Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \arcsin (x) \, dx=x \arcsin \left (x\right ) + \sqrt {-x^{2} + 1} \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \arcsin (x) \, dx=x \operatorname {asin}{\left (x \right )} + \sqrt {1 - x^{2}} \]
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none
Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \arcsin (x) \, dx=x \arcsin \left (x\right ) + \sqrt {-x^{2} + 1} \]
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none
Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \arcsin (x) \, dx=x \arcsin \left (x\right ) + \sqrt {-x^{2} + 1} \]
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Time = 0.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \arcsin (x) \, dx=x\,\mathrm {asin}\left (x\right )+\sqrt {1-x^2} \]
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