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int(cos5x+cos4x)/(1-2cos3x)dx " is equal...

` int(cos5x+cos4x)/(1-2cos3x)dx " is equal to "`

A

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

B

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

C

`-((cos2x)/(2)+cosx)+C`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`int(cos5x+cos4x)/(1-2cos3x)dx`
`=int(2cos.(9x)/(2)cos.(x)/(2)dx)/(1-2(2cos^(2)((3x)/(2))-1))`
`=int(2cos.(x)/(2)(4cos^(3),(3x)/(2)-3cos.(3x)/(2)))/(3-4cos^(2).(3x)/(2))dx`
`=-int2cos.(3x)/(2)cos.(x)/(2)dx=-intcos2xdx-int cosxdx`
`=-((sin2x)/(2)+sinx)+C`
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CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type
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  7. If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degre...

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  8. int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log(e)(f(x))+g(x)+C where C is the...

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  9. int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx equals

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  10. int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx gt0 is equal to

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  11. If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...

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  12. The value of int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx is

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  13. int(dx)/(xsqrt(x^(6)-16))=

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  14. int(dx)/(cos(2x)cos(4x))=

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  15. int x.2^(ln(x^(2)+1))dx is equal to

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  16. If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, ...

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  17. int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx equals

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  18. int((2x+1))/((x^(2)+4x+1)^(3//2))dx

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  20. The integral intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx equals

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