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IfI=intsqrt((5-x)/(2+x))dx ,t h e nIe q ...

`IfI=intsqrt((5-x)/(2+x))dx ,t h e nIe q u a l` `sqrt(x+2)sqrt(5+x)+3sin^(-1)sqrt((x+2)/3)+C` `sqrt(x+2)sqrt(5-x)+7sin^(-1)sqrt((x+2)/7)+C` `sqrt(x+2)sqrt(5-x)+5sin^(-1)sqrt((x+2)/5)+C` none of these

A

`sqrt(x+2)sqrt(5-x)+3sin^(-1)sqrt((x+2)/(3))+C`

B

`sqrt(x+2)sqrt(5-x)+7sin^(-1)sqrt((x+2)/(7))+C`

C

`sqrt(x+2)sqrt(5-x)+5sin^(-1)sqrt((x+2)/(5))+C`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
B
`"Put " 2+x=t^(2), " so that "dx=2tdt. " Then " `
` I=int(sqrt(7-t^(2)))/(t)(2t)dt=2int sqrt(7-t^(2))dt`
`=tsqrt(7-t^(2))+7sin^(-1)((t)/(sqrt(7)))+C`
`=sqrt(x+2)sqrt(5-x)+7sin^(-1)((sqrt(x+2))/(sqrt(7)))+C`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. int(sinx)/(sin(x-(pi)/(4)))dx " is equal to "

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  2. Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

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  3. 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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  4. int(sin2x)/(sin5xsin3x)dx is equal to

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  5. int(dx)/(x(x^n+1)) is equal to

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  6. Evaluate:int (dx)/(sqrt (sin^3 xsin(x+alpha)

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

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

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

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

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

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  13. Evaluate: int (sqrt(tanx)+sqrtcotx)dx

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  14. IfI=int(sin2x)/((3+4cosx)^3)dx ,t h e nIe q u a l s (3cosx+8)/((3+4co...

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  15. 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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  16. intsqrt(e^x-1)dx is equal to (a) 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+...

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  17. Evaluate: int((1+x^2)/(x^2-x^4))dx

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  18. int(sqrt(x^2+10 x+24))/(x+5)dx is equal to

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  19. The value of int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is "

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  20. "If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...

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