Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

Similar Questions

Explore conceptually related problems

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

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

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

int(x^(2))/((xsin x+cosx)^(2))dx is equal to

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

int(cosx-sinx)/(1+2sin x cosx)dx is equal to

int(1-cosx)cosec^(2)x dx is equal to