" (9) "int_(1/e)^(e)lg xdx

int_(1)^(e)log xdx=.......

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

" (a) "int e^(x)cos xdx

I=int_(-1)^1e^xdx

int(e^(2x)+1)/e^xdx

Evaluate : int_(0)^(∞)( e^xdx)/ ( 1 + e^(2x) )

Evaluate b int_(1)^(e){(1+x)e^(x)+(1-x)e^(-x)}ln xdx

int_(e)^(e^(2))(log xdx)/((1+log x)^(2))=(e)/(6)(2e-3)

int e^(x)cos^(2)xdx