2 x-3 x/6 x+4 x - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 46 of 271

Marks: +1, -0

\frac{2\cos x-3\sin x}{6\cos x+4\sin x}

Solution:

Let

I=\int \frac{2\cos x-3\sin x}{6\cos x+4\sin x}dx

\frac{1}{2}\int \frac{2\cos x-3\sin x}{2\sin x+3\cos x}

Put

2\sin x+3\cos x=t

\Rightarrow (2\cos x-3\sin x)dx=dt

\therefore I=\frac{1}{2}\int \frac{dt}{t}=\frac{1}{2}\log{|t|}+C

=\frac{1}{2}\log{|2\sin x+3\cos x|}+C

Go to Question: