" 19."(e^(2t)-1)/(e^(in)+1)

int_ (0)^(4 pi) e^(t) (sin^(6) at+cos^(4) at) dtint_ (0)^(pi) e^(t) (sin^(6) at+ cos^(4) at) dta = 2, L = (e^(4 pi) -1)/(e^(pi) -1) (ii) a = 2, L = (e^(4 pi)+ 1)/(e^(pi) +1) (iii) a = 4, L = (e^(4 pi) -1)/(e^(pi) -1) (iv) a = 4, L = (e^(4 pi) +1)/(e^(pi) +1)

" 19."int(1)/((e^(x)-1)(e^(x)+3))dx

lim_(t rarr oo)(e^(t^(2))-1)/(e^(t^(2))+1)

Q.6 lim_(t rarr oo)(e^(t^(2)-1))/(e^(t^(2)+1))

Let f(x) = (e^(x)+1)/(e^(x)-1) and int_0^(1)( (e^(x)+1)/(e^(x)-1)) x dx = lambda , then int_(-1)^(1) t f(t) dt =

Let A = int_0^(1) e^(t)/(t+1) dt , then int_0^(1) (t.e^(t^(2)))/(t^(2)+1) dt =

Integrate the functions e^(t)((1)/(t)-(1)/(t^(2)))

Prove that (tan^(-1)(1)/(e))^(2)+(2e)/((e^(2)+1))<(tan^(-1)e)^(2)+(2)/(sqrt(e^(2)+1))

Find the eccentricity of the hyperbola given by equations x=(e^(i+e^(-1)))/(2) and y=(e^(t)-e^(-1))/(3),t in R

If int_(0)^(1)(e^(t))/(1+t)dt=a, then find the value of int_(0)^(1)(e^(t))/((1+t)^(2))dt in terms of a