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int(sqrt(x-1))/(x sqrt(x+1))dx " is equa...

`int(sqrt(x-1))/(x sqrt(x+1))dx " is equal to "`

A

`"Ln "|x-sqrt(x^(2)-1)|-tan^(-1)x+c`

B

`"In "|x+sqrt(x^(2)-1)|-tan^(-1)x+c`

C

`"In "|x-sqrt(x^(2)-1)|-sec^(-1)x+c`

D

`"In "|x+sqrt(x^(2)-1)|-sec^(-1)x+c`

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int(sqrt(x-1))/(xsqrt(x+1))dx=int(x-1)/(xsqrt(x^(2)-1))dx`
`=int(dx)/(sqrt(x^(2)-1))-int(dx)/(xsqrt(x^(2)-1))`
`="In " |x+sqrt(x^(2)-1)|-sec^(-1)x+c`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
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  2. If intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l co...

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  3. int(sqrt(x-1))/(x sqrt(x+1))dx " is equal to "

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  4. IfI=int(dx)/(secx+cos e cx),t h e nIe q u a l s 1/2(cosx+sinx-1/(sqr...

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  5. int("sin"(5x)/(3))/("sin"(x)/(2))dx is equal to (where, C is a constan...

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  6. int (cos 5x + cos 4x)/(1-2cos3x) dx

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  7. IfI=intsqrt((5-x)/(2+x))dx ,t h e nIe q u a l sqrt(x+2)sqrt(5+x)+3si...

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  8. int(sin2x)/(sin5xsin3x)dx is equal to

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  9. int(dx)/(x(x+1)) is

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  10. Evaluate: int1/(sqrt(sin^3xsin(x+alpha)))\ dx ,\ alpha!=npi,\ \ n in ...

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  11. int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx is equal to (1...

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  12. If y=int1/(1+x^2)^(3/2)dx and y=0 when x=0 , then value of y when x=1 ...

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  13. int sqrt(x)(1+x^(1//3))^(4)dx " is equal to "

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  14. int(In(tanx))/(sinx cosx)dx " is equal to "

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  15. If m is a non-zero number and int (x^(5m-1)+2x^(4m-1))/(x^(2m)+x^m+1)^...

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  16. If l^(prime)(x) means logloglog x , the log being repeated r times, th...

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  17. Find int[sqrt(cotx)+sqrt(tanx)]dx

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  18. If I= int (sin 2x)/((3+4cosx)^(3))dx, then I equals

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  19. int(ln((x-1)/(x+1)))/(x^2-1)dxi se q u a lto 1/2(ln((x-1)/(x+1)))^2+...

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  20. int sqrt(e^(x)-1)dx is equal to

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