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

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:

A

Divide numerator and denominator by `sin^(2)x`, then
`int(("3 cosec"^(2)x+"2 cosec x cot x"))/(("2 cosec x "+3 cot x)^(2))dx`
Put `" 2 cosec x "+"3 cot x = t`
` therefore" "(-"2 cosec x cot x "-"3 cosec"^(2)x)dx=dt`
`=int-(dt)/(t^(2))=(1)/(t)+C=(1)/("2 cosec x"+"3 cot x")+C`
`=(sinx)/((2+3 cos x))+C`

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Knowledge Check

int(3+2cos x)/((2+3cosx)^(2))dx=

A

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

B

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

C

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

D

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

int(cos2x)/((sinx+cosx)^(2))dx is equal to

A

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

B

`log(sinx+cosx)+C`

C

`log(sinx-cosx)+C`

D

`log(sinx+cosx)^(2)+C`

The value of int(cos2x)/(sinx+cosx)^(2) dx is equal to

A

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

B

`ln(sinx+cosx)+C`

C

`ln(sinx-cosx)+C`

D

`ln(sinx+cosx)^(2)+C`

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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-INTEGRATION -PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)

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