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pl inegrate sqrt( x/(x-1))

aditya_arora04

Hi,

Look,

i am not using the integration sign, assume it to be present :

sqrt( x/(x-1))

x/(x*(x-1))^1/2

2x-1+1/[2(x*(x-1))^1/2 ]

put x(x-1) = t

So, dt = (2x-1) dx

So,

dt/[2(t)^1/2 ] + 1/[2(x*(x-1))^1/2 ] leave the second expression as it is now.

first can be easily integrated now.

For second, amke it a perfect square and then use the special integration formulae to get the final answer

P90

In ur question initially substitute x=sec²A.

then denominator will be tan²A

the integral will reduce to (sec²A/tan²A)^1/2.

but as x=sec²A---------->> dx=( 2secA * secA * tanA)da

so the final integral will look like (secA / tanA)* dx which will lead 2 cancellation

of tanA resulting in --------------->

2sec³A dA------------> now rewrite the same in terms of cosA and next integral will luk like

2/cos³A dA, express this as 2cosA/cos⁴A dA now express denom as (1-sin²A)*(1-sin²A). Now finally put sinA as ' t ' then cosA dA will be dt and the end result will be

2dt / (1-t²)(1-t²).Use partial fractions and finish it!!!

Hope my detailed steps help u . Rate me if u feel dey helped u.

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