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

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

A

`cosx+(1)/(2)cos2x-(1)/(3)cos3x+C`

B

`cosx-(1)/(2)cos2x-(1)/(3)cos3x+C`

C

`cosx+(1)/(2)cos2x+(1)/(3)cos3x+C`

D

`cosx-(1)/(2)cos2x+(1)/(3)cos3x+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int 4sinx "cos"(x)/(2)"cos"(3x)/(2)dx `
`=int 2sinx(cos2x+cosx)dx`
`=int(sin 3x-sinx+sin2x)dx`
`=cosx-(1)/(3)cos 3x-(1)/(2)cos2x+C`
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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. int(sqrt((a+x)/(a-x))+sqrt((a-x)/(a+x)))dx " is equal to "

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

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

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  4. "If " int sqrt(1+sinx) f(x)dx=(2)/(3)(1+sinx)^(3//2)+c, " then " f(x) ...

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

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

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  8. Evaluate: int(cos5x+cos4x)/(1-2cos3x)dx

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  9. 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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  10. int(sin2x)/(sin5xsin3x)dx is equal to

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

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

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

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

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

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

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  18. If l^r(x) means logloglog.......x being repeated r times, then int [ (...

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

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

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