integration/:>

1) multiplying denominator and numerator with sec²x ,

I = ∫sec²x dx4tan²x +4tanx +5

now put tanx =z , sec²xdx=dz

I = ∫dz4z²+4z+5

you can finish it off from here .

2) is x an integer ?

For two, @Aditya, I think he meant any general x.

Let x = n + f , n ε N

The Integration is ^n+f₀ ∫2^{t} dt, where {t} = Fractional part

I think this can be re written as n ₀¹âˆ« 2^t dt + ^0f∫2^t dt

thnks aditya dnt knw what was i thnkng .....
i can do d rest knw .
and @ vivek i gt ur pt and the ans too thnks fr the soln