Question

what is integration of sin inverse x

Answer 1

the integration of sin inverse is  

sin−1x=t⇒x=sint⇒dx=costdt

Then, the given integration becomes

∫tcostdt=t(sint)−∫tsintdt⇒∫tcostdt=t(sint)−[t(−cost)−∫t(−cost)dt]⇒∫tcostdt=tsint+tcost+C−∫tcostdt
⇒2∫tcostdt=tsint+tcost+C⇒∫tcostdt=t2sint+t2cost+C

Substituting sin−1x=t, we have:-

∫sin−1xdx=xsin−1x2+xx2−1√2+C

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Mahek Kantor answered this
13 helpful votes in Math, Class XII-Science

use the ilate method .

so it is 1 * sin-1 X

so take sin-1X as the first func. and '1' as the second

:)

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Kshitij Choudhary answered this
7 helpful votes in Math, Class XII-Science

put x =sint

dx=sintdt

then it is =integration of tsintdt

now us by parts and integrate

and substitute in final answer

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