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int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x...

`int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx` is equal to
(1)   `-x^p/(x^(p+q)+1)+C`    (2)   `x^q/(x^(p+q)+1)+C`   
(3)   `-x^q/(x^(p+q)+1)+C`    (4)   `x^p/(x^(p+q)+1)+C`   

Text Solution

Verified by Experts

The correct Answer is:
C
`int(px^(p+2q-1)-qx^(q-1))/((x^(p+q)+1)^(2))dx=int(px^(p-1)-qx^(q-1))/((x^(p)+x^(-q))^(2))dx " " ("Dividing "N^(r)" and "D^(r) " by "x^(2q))`
`=int(dt)/(t^(2))= -(1)/(t)+C, " where " t=x^(p)+x^(-q)`
`= - (1)/(x^(p)+x^(-q))+C`
`= -(x^(q))/(x^(p+q)+1)+C`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. int(dx)/(x(x^n+1)) is equal to

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

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

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

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

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

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

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

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

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

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

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

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

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  16. "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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  17. Evaluate: int(sin2x)/(sin^4x+cos^4x)dx

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  18. int(x+2)/((x^2+3x+3)sqrt(x+1))dx is equal to 1/3tan^(-1)(x/(sqrt(3(x+1...

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  19. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (2x+A...

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  20. int(cos2x)/((e^(-x)+cosx)sqrt(1+sin2x))dx,x in(0,(pi)/(2)) is equal t...

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