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int(3+2cosx)/((2+3cosx)^2)dx is equal to...

`int(3+2cosx)/((2+3cosx)^2)dx` is equal to (a) `((sinx)/(3cosx+2))+c` (b) `((2cosx)/(3sinx+2))+c` (c) `((2cosx)/(3cosx+2))+c` (d) `((2sinx)/(3sinx+2))+c`

A

`((sinx)/(3cosx+2))+c`

B

`((2cosx)/(3sinx+2))+c`

C

`((2cosx)/(3cosx+2))+c`

D

`((2sinx)/(3sinx+2))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
`"Let " I=int(3+2cosx)/((2+3cosx)^(2))dx. `
`"Multiplying " N^(r) " and " D^(r) " by " "cosec"^(2)x, " we get "`
`I=int((3"cosec"^(2)x+2cotx"cosec"x))/((2"cosec"x+3cotx)^(2))dx `
`=-int(-3"cosec"^(2)x-2cotx"cosec"x)/((2"cosec"x+3cotx)^(2))dx `
`=(1)/(2"cosec"x+3cotx)+C=((sinx)/(2+3cosx))+C`
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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  3. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c (b...

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  7. "I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c

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  8. If int(dx)/((x+2)(x^(2)+1)) = alog|1+x^(2)|+btan^(-1)x+ 1/5log|x+2|+C,...

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  9. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

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  12. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b , th...

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  13. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

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  14. int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3...

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  17. int(sqrt(x^2+1))/(x^4)dx=

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  19. The integral int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx is equal to-

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  20. If In=int( lnx)^n dx then In+nI(n-1)

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