a) Find the indefinite integral of the function 1 y = 3t2 + 2e3t + -+ 2 cos 3t b) Calculate the definite integral 2
(3t2 + 2e3t + - + 2 cos 3t} dt t

If you have any doubt please comment.

Step-by-step explanation

Given !- a ) gnidebinate integral of the function y = 3t2 + 2 e3 * + + 2 co13t. ydt = ( 3 + 2 + 2 ( 3# + 1 + 2 Cos3+ ) at 3+ 2 3 + 2 236 + Initl + 2 sinst + c. 3 ( ydt = + 3 + 2 3* + Loft) + 2 sinst + c formulas Used And " + 3 + 23 6 *+ Inll + 2 sinst + c 3 n+ 1 c dt : eat a 6 ) Debinate intechal of . Gnat at : sinal J ( 3 + 2 + 2 0 37 + 1/* + 2 cost ) at a = ( +3 + 2/ eat 8 + *x * Loltl + 2 sinst ), 2 23 + 2 - 3 * 2 + In121 + 2 sim (3x 2 ) ) ( 13 + 2 e 3 x 1 + 10/11 + 2 sin ( 3x1 ) ) = 7 + ( e - es + sin6 - sin3 ) + Ln 2 2 262 . 97 . .. 2 ( 3 + 2 + 2c ( + 1, + 2 cos 3 + ) dt : 26 2- 97.