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I =int (sin ^(8) x- cos ^(8) x)/( 1-2 si...

`I =int (sin ^(8) x- cos ^(8) x)/( 1-2 sin ^(2) x cos ^(2)x ) dx` is equal to:

A

`(1)/(2)sin2x+C`

B

`-(1)/(2)sin2x+C`

C

`-(1)/(2)sinx+C`

D

`-sin^(2)x+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(sin^(8)x-cos^(8)x)/(1-2sin^(2)xcos^(2)x)dx=int((sin^(2)x-cos^(2)x)(sin^(4)x+cos^(4)x))/(1-2sin^(2)xcos^(2)x)`
`=int-cos2xdx=-(1)/(2)sin2x+C`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  2. If int(cos4x+1)/(cotx-tanx)dx = Acos4x+B ,t h e n (a)A=-1/8 (b) B=1/...

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

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  4. int sqrt(1+sinx)dx " is equal to "

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  5. Evaluate: int((3sinx-2)cosx)/(5-cos^2x-4sinx)dx

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  6. 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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  7. int(sqrt(x-1))/(xsqrt(x+1))dx is e q u a l to ln|x-sqrt(x^...

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  8. IfI=int(dx)/(secx+cos e cx),t h e nIe q u a l s

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  9. int(sinx)/(sin(x-(pi)/(4)))dx " is equal to "

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

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  11. 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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  12. int(sin2x)/(sin5xsin3x)dx is equal to

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

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

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

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

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

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

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

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