Question

what is the answer ​

Answer 1

Explanation:

∫

2x−x

2

dx

=∫

1−(x−1)

2

dx

Substitute x−1=sinθ⇒dx=cosθdθ

∫

1−(x−1)

2

dx

=∫

1−sin

2

θ

cosθdθ

=∫

cosθ

cosθdθ

=∫dθ=θ+C ......... [Where C is a constant]

But θ=sin

−1

(x−1)

∴∫

2x−x

2

dx

=sin

−1

(x−1)+C