Verified answer

Please note that e^(2lnx) = e^(lnx²) = x², so the denominator of x² simply cancels out with that simplified part of the numerator. Thus, the integral is ∫cosx dx = sinx+C!!

You're going to slap yourself....

e^(2 ln x) = x^2 .... restricted to the domain x>0 so ln x is defined.

So, the x^2 terms cancel, and the integral of cos x dx is sin x + C.

e^2lnx = x^2

∫ cos x x^2 /x^2 = ∫ cos x = sin x + C

...cos(x)e^[2ln(x)]

∫---------------------------dx

..........x^2

.......cos(x)e^[ln(x)^2]

= ∫ -----------------------------dx

...............x^2

........cos(x)* x^2

= ∫ ----------------------dx

..............x^2

= ∫ cos(x)dx

= sin(x) + C answer//

y=sinx+C