Home
Class 12
MATHS
int((2+secx)secx)/((1+2secx)^2)dx=...

`int((2+secx)secx)/((1+2secx)^2)dx=`

A

`(1)/("2 cosec x"+cotx)+C`

B

`"2 cosec x"+cotx+C`

C

`(1)/("2 cosec x"-cotx)+C`

D

`"2 cosec x"-cotx+C`

Text Solution

Verified by Experts

The correct Answer is:
A

`I=int((2cosx+1))/((2+cosx)^(2))dx`
`=int((2+cosx)cosx+sin^(2)x)/((2+cosx)^(2))dx`
`=int(cosx)/(2+cosx)dx-int(-sin^(2)x)/((2+cosx)^(2))dx`
`=(sinx)/(2+cosx)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos
  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos
  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos
  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos
  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate int(secx(2+secx))/((1+2secx)^(2))dx

(secx-1)(secx+1)

int(secx cosec x)/(log(cotx))dx=

int(secx" cosec "x)/(log(tanx))dx

intx^(2)secx^(3)dx=

int 1/secx dx

intsecx/(secx+tanx)dx

int(secx)/(log(secx+tanx))dx=

The value of lim_(xrarr2pi)(1-(secx)^(secx))/(ln(secx)) is equal to