\int \frac{2 \tan x+3}{ \sin ^2 x+2 \cos ^2 x} \dx=

Correct Answer is : 3√2tan−1(tanx√2)+ln|tan2x+2|+C

{3}/{\sqrt{2}} \sin ^{-1} ( { \sin x}/{\sqrt{2}}) +\ln {| \sin ^2 x+2 |}+C

{3}/{\sqrt{2}} \tan ^{-1} ( {\tan x}/{\sqrt{2}}) +\ln {| \tan ^2 x+2 |}+C

{1}/{\sqrt{2}} \tan ^{-1} ( {\tan x}/{\sqrt{2}}) -\ln {| \tan ^2 x+2 |}+C

{3}/{\sqrt{2}} \cos ^{-1} ( {\cos x}/{\sqrt{2}}) +\ln {| \sin ^2 x+2 |}+C

{1}/{\sqrt{2}} \cos ^{-1} ( {\cos x}/{\sqrt{2}}) -\ln {| \cos ^2 x+2 |}+C

KEAM 2023 Math Solved Paper

Question : 88 of 120

Marks: +1, -0

∫‌

2‌tan‌x+3

sin‌2x+2cos2x

‌dx=

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