need assistance on 2-3 thank you

1. Use the definition of an improper integral to evaluate the following integrals. (a) J x-3 dx (b) So xsiz dx (c) J. x3/2 dx 2. Determine whether the improper integral is convergent or divergent without solving the integral. Use an appropriate inequality to support your conclusion. ( a) hix +3x' +2 dx 2x 1 ( b ) 2 vx- Id 3. Complete the square in the denominator, make appropriate substitution, and integrate. 2x - 3 Jx2 + 4x +5 dx (Hint:) 4. Evaluate the following integrals using the integration by parts. (a) S(3x + 4) sin xdx (b) S2xInxdx (c) fx'edx 5. Find the integral fe" sin(x)dx (Hint: Reappearing Integral)