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  • Integrate: 2 tan x +3 / sin^2 x + 2cos^2 x

Integrate: 2 tan x +3 / sin^2 x + 2cos^2 x

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Solution:

            I=int frac2 an x+3 sin^2x+2cos^2xdx

Dividing the numerator and denominator by cos^2x  and 

substituting      an x=tRightarrow sec^2xdx=dt

            I=int frac2 an x+3 sin^2x+2cos^2xdx=int frac(2 an x+3)sec^2x an^2x+2dx\ \ Rightarrow hspace1cmI=int frac2t+3t^2+2dt=ln (t^2+2)+frac3sqrt2 an^-1fractsqrt2+c\ \ Rightarrow hspace1cmI=ln ( an^2x+2)+frac3sqrt2 an^-1frac an xsqrt2+c

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Deependra Verma

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