Homework 6- Additional ExercisesProblems 1-5 regard partial fraction decomposition (see section 7.4), problems 6-9 regard improper integrals (see section 7.8), and problem 10 regards arc length (see section 8.1).Evaluate 01x-1x23x2dx.Evaluate x3x31dx.Use integration by parts, together with the techniques of this section, to evaluate ln(x2-x2)dx.Karl Weierstrauss (1815-1897) noticed that the substitution t=tan(x2) will convert any rational function of sinx and cosx into an ordinary rational function of t.(a) If cos(x2)=11t22, and ,sin(x2)=t1t22cosx=1-t21t2,,sinx=2t1t2dx=21t2dtt13-5sinxdx6-8-012x-5dx--112-w2dw--1e-2tdt0e-x2dx=01-lny2dy,y=ln(1-x2)x=0x=12t=tan(x2),-, sketch a right triangle or use trigonometric identities to show thatcos(x2)=11t22, and ,sin(x2)=t1t22(b) Show that cosx=1-t21t2, and ,sinx=2t1t2.(c) Show that dx=21t2dt.5. Use the Weierstrauss substitution described above to transform the integral into a rational function oft and then evaluate the integral13-5sinxdxIn problems 6-8, evaluate the integral, ifit converges, or prove that it diverges.6.-012x-5dx7.--112-w2dw8.--1e-2tdt9. Show that 0e-x2dx=01-lny2dy,by interpreting these integrals as areas of plane regions.10. Find the exact length of the graph ofy=ln(1-x2) from x=0tox=12. I NEED 2,3,4,5,10. ONLY