Home
Class 12
MATHS
Evaluate: int(cosx)/(sqrt(sin^2x-2sinx-3...

Evaluate: `int(cosx)/(sqrt(sin^2x-2sinx-3))\ dx`

Text Solution

Verified by Experts

I= `int(cosx)/(sqrt(sin^2x-2sinx-3))\ dx`
I= `int(cosx)/(sqrt((sinx-1)^2sinx-2^2))\ dx`
Let `sinx−1=t`
`⇒cosx.dx=dt`
Substituting we get-
`I=int (dt)/(sqrt(t^2-2^2))`
`=log∣t+sqrt(t^2−2^2)​∣​+C`
`=log∣​(sinx−1)+sqrt((sinx−1)^2−4 ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

Evaluate: (i) int(e^x)/(sqrt(5-4\ e^x-e^(2x)))\ dx (ii) int(cosx)/(sqrt(sin^2x-2sinx-3))\ dx

Evaluate: int(cosx)/(sin^2x+4sinx+5)\ dx

Knowledge Check

  • int(cosx)/(sqrt(sin^2x-sinx-3))dx=

    A
    `log|sinx+1+sqrt(sin^2-2sinx-3)|+c`
    B
    `log|sinx+1-sqrt(sin^2-2sinx-3)|+c`
    C
    `log|sinx-1+sqrt(sin^2-2sinx-3)|+c`
    D
    `log|sinx-1-sqrt(sin^2-2sinx-3)|+c`

  • int(cosx)/(sqrt(sin^2x-2sinx+5))dx=

    A
    `log|sinx-1+sqrt(sin^2x-2sinx+5)|+c`
    B
    `-log|sinx-1+sqrt(sin^2x-2sinx+5)|+c`
    C
    `log|sinx+1+sqrt(sin^2x+2sinx+5)|+c`
    D
    `-log|sinx+1+sqrt(sin^2x+2sinx+5)|+c`

    • Similar Questions

    Explore conceptually related problems

    Evaluate: int(sinx+cosx)/(sqrt(1+sin2x))\ dx

    Evaluate: int(cosx-sinx)/(sqrt(8-sin2x))\ dx

    Evaluate int(cosx)/((sin^(2)x+4sinx+5))dx .

    Evaluate: int(sinx-cosx)/(sqrt(sin2x))\ dx

    Evaluate int cosx/(sqrt(25-sin^2x)) dx

    Evaluate int((sinx+cosx)dx)/(sqrt(3+sin2x)).

    Home
    Profile