Integration of (1+x-2x 2 ) 1/2 dx Integration of sininversex/(1-x 2 ) 3/2

  1. Integration of (1+x-2x2)1/2dx
  2. Integration of sininversex/(1-x2)3/2

Grade:12th pass

2 Answers

425 Points
4 years ago
Look at the denominator term within root.Try to write it as two whole square terms.
So the integration becomes
\frac{1}{2}\int \frac{dx}{\sqrt{(3/4)^2-(x-1/4)^2}}
425 Points
4 years ago
In the 2nd integration put
So, dz=\frac{dx}{\sqrt{1-x^2}}
Also x=sinz
put these values in the integration.It will become
=\int\ z sec^2z dz
Now do integration by parts.Take z as 1st function.
\int\ z sec^2z dz
=ztanz-\int tanz dz
Please approve the answer if it helps you.

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