Evaluate the following definite integrals (1-58): `int_1^2 1/(sqrt((x-1)(2-x)))dx`

Explanation

`I=int_1^2 1/(sqrt((x-1)(2-x)))dx`

`I=int_1^2 1/(sqrt(-x^2+3x-2))dx`

`I=int_1^2 1/(sqrt(-[(x-3/2)^2-(1/2)^2])dx`

`I=int_1^2 1/(sqrt([(1/2)^2-(x-3/2)^2])dx`

So,

`int1/(sqrt(a^2-x^2))=sin^(-1)(x/a)`


Thus,

...