Home
Class 12
MATHS
(cos x)/(sqrt(1+sin x))...

`(cos x)/(sqrt(1+sin x))`

Text Solution

AI Generated Solution

To solve the integral \(\int \frac{\cos x}{\sqrt{1 + \sin x}} \, dx\), we will follow these steps: ### Step 1: Set up the integral Let \( I = \int \frac{\cos x}{\sqrt{1 + \sin x}} \, dx \). ### Step 2: Use substitution We will use the substitution \( t = 1 + \sin x \). Then, we differentiate \( t \) with respect to \( x \): \[ ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.3|24 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.4|25 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.1|22 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

Solve the following integration int (sin x+cos x)/(sqrt(1+sin 2x))*dx , here (sin x + cos x) gt 0

The minimum value of the function f(x)=(sinx)/(sqrt(1-cos^2x))+(cosx)/(sqrt(1-sin^2x))+(tanx)/(sqrt(sec^2x-1))+(cotx)/(sqrt(c o s e c^2x-1)) whenever it is defined is

Evaluate : int ("cos 2x ")/(sqrt(1+ "sin" 2x))" dx "

Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) = (x)/(2), x in (0, (pi)/(4))

The total number of solutions of cos x= sqrt(1- sin 2x) in [0, 2pi] is equal to

Find the range of f(x)=sqrt(sin(cos x))+sqrt(cos(sin x)) .

cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]=

int(sin x)/( sqrt(1+cos x))dx=?

Evaluate: int_0^(pi//2)(sqrt(sin x))/(sqrt(sin x)+sqrt(cos x))dx

If 2y=(cot^(-1)((sqrt3 cos x + sin x)/(cos x - sqrt3 sin x)))^(2) , x in (0, pi/2) " then " (dy)/(dx) is equal to