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Mathematics Unit 2 SA1: Integration 2/2021 Rule 3 : Antiderivatives of Exponential Functions Sex dx = ex +c [earth dx = _eax a Examples : Sex+3 dx = Le 2x+3 + c [ 3e 4- 2x dx = - 2e4-2x + c V y dx [e' dx [e 3x dx [e -ox dx MONASH University Foundation Year [ Vest dx pathway to Monash Uni [ V2et dx [ 4(e* + 1) dx [ (e tex -ex) dx [(2ex - V2ex + 1) or )dx Sex- ext- dx 2e MUFY @SC Path Way to a Brighter Future Page 85 of 199Mathematics Unit 2 SA1: Integration 5 2/2021 Rule A : Antiderivatives of Circular Functions [ sinx dx = -cosx + c [sin(ax) dx = -- cos(ax) + c [cosx dx = sin x + c [ cos(ax) dx = - sin(ax) +c Examples: sin 2x dx = -- cos2x + c 2 3cos 4x dx =- sin 4x + c Find antiderivatives of the following: (sin 3x + sin 4x)dx 2 { ( - 2cos * ) dx MONASH University Foundation Year 3. (2cos-x+ - sin 3x) dx 4 . Isin (2xx) dx 34 pathway to Monash University [ V3mecos(ex) dx ( sin To + 2 cos 2x) dx 5 . 7. (cos(-3x) + 2sinx) dx 8 . sin (2x - 7) dx Page 86 of 199 Path Way to a Brighter Future MUFY@SC