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Evaluate : int(e^xdot(2+sin2x)/(2cos^2x)\ dx

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Solution :
Let `I = int ( e^x(2+sin2x))/(2cos^2x) dx`<br> `=> I = int (e^x/cos^2x + (e^xsin2x)/(2cos^2x) dx)`<br> `=> I = int (e^x/cos^2x + (e^x(2sinxcosx))/(2cos^2x) dx)`<br> `=> I = int (e^xsec^2x + e^xtanx)dx`<br> Let `e^xtanx = t, `then <br> `=>(e^x(sec^2x) + tanx(e^x)) dx = dt`<br> `=> (e^xsec^2x + e^xtanx)dx = dt`<br> `:. I = int dt `<br> `=> I = t+c`<br> `=>I = e^xtanx+c`<br>

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