1.

Evaluate ∫ sec6x dx

Answer»

∫ sec6x dx

In this integral we will use the formula,

1+tan2x = sec2x

I = ∫sec2x sec4x dx 

= ∫sec2x (1 + tan2x)2dx 

Now, 

Put tan x = t which means sec2xdx = dt, 

I = ∫(1+ t2)2dt 

= ∫(1+t4+2t2) dt 

Now put the value of t, 

which is t = tan x in above integral-

I = tanx + \(\frac{tan^5x}{5}\)+ 2.\(\frac{tan^3x}{3}\)



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