Evaluate the following integrals. \int \frac{dx}{\sqrt{(x-1)(3-x)}}

Tabansi 2020-10-23 Answered
Evaluate the following integrals.
dx(x1)(3x)
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Expert Answer

Neelam Wainwright
Answered 2020-10-24 Author has 102 answers
Step 1: Given that
dx(x1)(3x)
Step 2: Formula Used
1a2x2dx=sin1(xa)+C
Step 3: Solve
We have,
dx(x1)(3x)=dx3xx23+x
=dxx2+4x3
=dx(x24x+3)
=dx(x24x+2222+3)
=dx((x2)24+3)
=dx((x2)21)
=dx1(x2)2
=sin1(x2)+C

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