If `x=1-sqrt(2),fin dt h ev a l u eof(x-1/x)^3`

If sin(A-B)=1/(sqrt(10 ,))cos(A+B)=2/(sqrt(29)),fin dt h ev a l u eof2Aw h e r eAa n dBl i eb e t w e e n0a n dpi/4dot

F in dt h ev a l u eofint_0^1logx dxdot

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

L e tA=int_0^oo(logx)/(1+x^3)dxdotT h e nfin dt h ev a l u eofint_0^oo(xlogx)/(1+x^3)dx in terms of Adot

f(x)=int_1^x(tan^(-1)(t))/t dtAAx in R^+,t h e nfin dt h ev a l u eof f(e^2)-f(1/(e^2))

Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [x] is the greatest integer less than or equal to xdot If I=int_(-1)^2(xf(x^2))/(2+f(x+1))dx ,t h e nt h ev a l u eof(4I-1)i s

Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(cos^2x)dx ,t h e nfin dt h ev a l u ekdot

Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(cos^2x)dx ,t h e nfin dt h ev a l u ekdot

Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(c0s^2x)dx ,t h e nfin dt h ev a l u ekdot

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof|(dy)/(dx)-x((dy)/(dx))^3| is__________