Pueden resolver esta integral con todos los pasos porfavor?

<img src="https://tex.z-dn.net/?f=%5Cbold%7B%5Cint%7B%5Csqrt%7B%5Cfrac%7Barcsenx%7D%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx%3D%5Cfrac%7B2%7D%7B3%7D%20%28arcsenx%29%5E%7B%283%2F2%29%7D%2BC%7D" />Explicación paso a paso : Vamos a aplicar el método de cambio de variable simple, dado que : <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%28arcsenx%29%7D%7Bdx%7D%3D%5Cfrac%7Bdx%7D%7B%5Csqrt%7B1-x%5E%7B2%7D%7D%7D" />Para ello, reescribimos el integrando de manera tal que la diferencial que se necesita se explicite en la integral : <img src="https://tex.z-dn.net/?f=%5Cint%7B%5Csqrt%7B%5Cfrac%7Barcsenx%7D%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx%3D%5Cint%7B%5Cfrac%7B%5Csqrt%7Barcsenx%7D%7D%7B%5Csqrt%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx" />Planteamos el siguiente cambio : <img src="https://tex.z-dn.net/?f=U%3Darcsenx%20%5Cqquad%20%5CRightarrow%20%5Cqquad%20%5Cfrac%7BdU%7D%7Bdx%7D%3D%5Cfrac%7Bdx%7D%7B%5Csqrt%7B1-x%5E%7B2%7D%7D%7D" />Volviendo a la integral : <img src="https://tex.z-dn.net/?f=%5Cint%7B%5Csqrt%7B%5Cfrac%7Barcsenx%7D%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx%3D%5Cint%7B%5Cfrac%7B%5Csqrt%7Barcsenx%7D%7D%7B%5Csqrt%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx%3D%5Cint%7B%5Csqrt%7BU%7D%7D%20%5C%2C%20dU" />Esta integral se resuelve por la formula de potencias : <img src="https://tex.z-dn.net/?f=%5Cint%7B%5Csqrt%7B%5Cfrac%7Barcsenx%7D%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx%3D%5Cint%7B%5Csqrt%7BU%7D%7D%20%5C%2C%20dU%3D%5Cint%7BU%5E%7B1%2F2%7D%7D%20%5C%2C%20dU%3D%5Cfrac%7B2%7D%7B3%7DU%5E%7B3%2F2%7D%2BC" />En definitiva : <img src="https://tex.z-dn.net/?f=%5Cbold%7B%5Cint%7B%5Csqrt%7B%5Cfrac%7Barcsenx%7D%7B1-x%5E%7B2%7D%7D%7D%7D%20%5C%2C%20dx%3D%5Cfrac%7B2%7D%7B3%7D%20%28arcsenx%29%5E%7B%283%2F2%29%7D%2BC%7D" />.