'. EXAMPLEZ Evaluate 1%de. Sin'L , SOLUTION This indefinite integral isn't immediately aaparent in the Table of Indefinite Integrals, so we use trigonometric identities to rewrite the function before a Z/(sinli'j) fcsq} cotIE') d8 integ rating: +C. 2 EXAMPLE 4 Find / (2XE 6x + )dx and interpret the result in terms of areas. 0 5 x2 + 1 SOLUTION The Fundamental Theorem gives 2 5 (2)376er )o'xi 0 x2+1 + 5 tan1(2). This is the exact value of the integral. If a decimal approximation is desired, we can use a calculator to approximate tan1(2). Doing so, we get 2 (2X3 6x + 5 )dx x . [Round your answer to four decimal places.)- 0 22 + 1 The figure below shows the graph of the integrand. We now.I that the value of the integral can be interpreted as a net area: the sum of the areas labeled with a plus sign minus the area labeled with a minus sign. Find the general indefinite integral. (Use C for the constant of integration.) 8 X2+1 4X2+3+ dX