How can I use integration by tables to solve sin^-1(sqrtx)?

[rmiller70015]

Homework Statement

Integrate sin^-1(sqrtx)

Homework Equations

The Attempt at a Solution

To solve this, I first made a substitution of u=arcsin(sqrtx) so dx=sqrt(1-u)du

Still pretty difficult to solve, so I integrated by parts with v=sqrt(1-u) dw=udu dv=(1/2)(sqrt(1-u))2 and w=(1/2)(u^2)
To integrate this new equation, I used a table to get this: sqrt(1-u)(1/2)(u^2) + (1/2)arcsinu + c

I put this all together and changed the u to arcsin(sqrtx).

I'm wondering if this was a legit way of solving this equation.

 

[scurty]

Homework Statement

Integrate sin^-1(sqrtx)

Homework Equations

The Attempt at a Solution

To solve this, I first made a substitution of u=arcsin(sqrtx) so dx=sqrt(1-u)du

You misused the Chain Rule here.

 

[rmiller70015]

You're right, I just saw that that will leave me with root 1-x du not 1-u, thanks