Math, asked by suzy10, 3 months ago

integral value of 2xdx /(x+1)(x-1))​


archincode: Let I=∫011−x1+x−−−√dx

=∫011−x1−x2√dx

=∫0111−x2√dx−∫01x1+x2√dx

=[sin−1x]10−∫01x1−x2√dx

Put t2=1−x2⇒2tdt=−2xdx

⇒tdt=−xdx

∴I=(sin−11−sin−10)+∫10ttdt

=π2+[t]01=π2−1

Answers

Answered by abhi569
0

Answer:

log |x^2 - 1| + C

Step-by-step explanation:

Solving the denominator:

Let, (x + 1)(x - 1) = t

x^2 - 1 = t , differentiate w.r.t x:

=> d(x^2 - 1)/dx = dt/dx

=> 2x dx = dt

Therefore,

=> 2x dx / (x + 1)(x - 1)

=> dt/t

=> log |t| + C

=> log |x^2 - 1| + C

Which can also be written as ln |x^2 - 1|

Answered by archincode
0

Answer:

Let I=∫011−x1+x−−−√dx

=∫011−x1−x2√dx

=∫0111−x2√dx−∫01x1+x2√dx

=[sin−1x]10−∫01x1−x2√dx

Put t2=1−x2⇒2tdt=−2xdx

⇒tdt=−xdx

∴I=(sin−11−sin−10)+∫10ttdt

=π2+[t]01=π2−1

Step-by-step explanation:

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