Question:
\(\int\frac{2\tan x+3}{\sin^2x+2\cos^2x}dx=\)
\(\int\frac{2\tan x+3}{\sin^2x+2\cos^2x}dx=\)
Updated On: Jun 10, 2024
- \(\frac{3}{\sqrt2}sin^{-1}\frac{\sin x}{\sqrt2}+ln|\sin^2x+2|+C\)
- \(\frac{3}{\sqrt2}tan^{-1}\frac{\tan x}{\sqrt2}+ln|\tan^2x+2|+C\)
- \(\frac{3}{\sqrt2}tan^{-1}\frac{\tan x}{\sqrt2}-ln|\tan^2x+2|+C\)
- \(\frac{3}{\sqrt2}cos^{-1}\frac{\cos x}{\sqrt2}+ln|\sin^2x+2|+C\)
- \(\frac{3}{\sqrt2}cos^{-1}\frac{\cos x}{\sqrt2}-ln|\cos^2x+2|+C\)
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The Correct Option is B
Solution and Explanation
The correct option is (B): \(\frac{3}{\sqrt2}tan^{-1}\frac{\tan x}{\sqrt2}+ln|\tan^2x+2|+C\)
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