\int \frac{1}{\cos x} [\frac{1}{ \sin x}-\frac{1}{ \sin x+3 \cos x}] \dx= [AP EAPCET 23 May 2025 S1]

Correct Answer is : log|sinxsinx+3cosx|+c

\frac{1}{3} \log {| \frac{ \sin x}{ \sin x+3 \cos x} |}+c

\log {| \frac{\cos x}{ \sin x+3 \cos x} |}+c

\frac{1}{3} \log {| \frac{\cos x}{ \sin x+3 \cos x} |}+c

\log {| \frac{ \sin x}{ \sin x+3 \cos x} |}+c

Indefinite Integration

Section: Mathematics

Question : 9 of 89

Marks: +1, -0

∫‌

cos‌x

[‌

sin‌x

−‌

sin‌x+3‌cos‌x

]‌dx=

[AP EAPCET 23 May 2025 S1]

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