The idea behind integration by parts depends on O Kirchoffs Rules O the chain rule O the product rule O The five-second rule O the quotient ruleRecall that the act of integrating by parts is appealing to this formula [f(x)g(x)da + / f(x)9(x) da = f(x)g(x). We try to compute the integral / x In(x)dx. If f(a) = a and g'(x) = In(x) then the other integral / f'(x)9(x) dx is O more complicated O equally complicated O less complicated If f'(a) = 2 and g() = In(x) then the other integral / f(x)g'(x)dx is O less complicated O equally complicated O more complicatedIn order to integrate x'edx, how many times must we integrate by parts before we get to an elementary integral?For each integral, choose the best u-substitution. The integral costsin' tdt is best computed by substituting u = O neither O sin(t) O cos(t) O either The integral cost sin'tat is best computed by substituting u = O neither O cos(t) O either O sin(t) The integral / sec* t tan tdt is best computed by substituting u = O either O tan(t) O neither O sec(t) The integral /sec' t tan' tdt is best computed by substituting u = O neither O sec(t) O either O tan(t)For each of the following integrals, indicate the best trigonometric substitution. 1 For 1 - 2 2 -dx, let x = O tan(t) O sec(t) O sin(t) For / (8 + 2x2) ? dac, let X = O 2 sin(t) O 2tan(t) O 2sec(t) 1 For dx, let x = (ac + 3)2 - 1 O sin(t)-3 O sec(t)-3 O tan(t)-3Fill in the blanks. For most functions f(x), computing the arc length area integral is by analytic methods. O impossible O hard O easy For most functions f(x) revolved around the x-axis, computing the surface area area integral is by analytic methods O hard O impossible O easy