{ x}{{1+ x}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 50 of 271

Marks: +1, -0

\frac{\cos x}{\sqrt{1+\sin x}}

Solution:

Let

I=\int \frac{\cos x}{\sqrt{1+\sin x}}dx

Put

\sin x = t

\Rightarrow \cos x dx = dt

\therefore I=\int \frac{dt}{\sqrt{1+t}}=\frac{(1+t)^{-1/2+1}}{-1/2+1}+C

=1(1+t)^{1/2}+C=2\sqrt{1+\sin x}+C

Go to Question: