1.

Evaluate the following integrals :\(\int\)\(\frac{2cos2x+sec^2x}{sin2x+tanx-5}\)dx

Answer»

Assume,

sin2x + tanx - 5 = t

d(tanx + sin2x - 5) = dt 

(2cos2x + sec2x) dx = dt 

Put t and dt in given equation we get

⇒ \(\int\frac{dt}{t}\)

= In|t| + c

But,

t = sin2x + tanx - 5 

= ln|sin2x + tanx - 5| + c.



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