University:
Whitman College
Course:
MATH-125 | Calculus I
Academic year:

2020
Views:

307

Pages:

2
Author:

rezancuk2j

AntiderivativesFormulaSheet 1 Basic Antiderivatives • Iff (x)=a thenF (x)=ax+ C • Iff (x)=xa thenF (x)= • Iff (x)= 1 x xa+1 + C (unlessa = −1) a+1 thenF (x)=ln(x)+C • Iff (x)=ex thenF (x)=ex + C • Iff (x)=cos(x)thenF (x)=sin(x)+C • Iff (x)=sin(x)thenF (x)=− cos(x)+C • Iff (x)=sec2 (x)thenF (x)=tan(x)+C 2 Antiderivatives Rules Iftheantiderivativeof f (x)isF (x),andtheantiderivativeof g(x)isG(x)then • Theantiderivativeofaf(x)+bg(x)isaF(x)+bG(x)(forany a, b) 1 • Theantiderivativeoff (ax+ b)is a F (ax+ b) Asaresult: • Iff (x)=(dx+ b)a thenF (x)= • Iff (x)= 1 ax+b thenF (x)= • Iff (x)=eax+b thenF (x)= (dx+b)a+1 1 d 1 a 1 • Iff (x)=cos(ax+ b)thenF (x)= a • Iff (x)=sec (ax+ b)thenF (x)= + C (unlessa = −1) eax+b + C 1 a • Iff (x)=sin(ax+ b)thenF (x)=− 1 2 a+1 ln(ax+ b)+C sin(ax+ b)+C a 1 a 1 cos(ax+ b)+C tan(ax+ b)+C 3 Intermediate Rules • Theantiderivativeof f ′ (x) f (x) isln[f (x)]+C • Theantiderivativeoff ′ (x)f a (x)is cialcases”ofthisrule: f a+1 (x) – Theantiderivativeoff ′ (x)f (x)is – Theantiderivativeof – Theantiderivativeof 1 f ′ (x) √ . Thefollowingareuseful“spe- a+1 2 f 2 (x) p is2 f (x) f (x) f ′ (x) is− 1f (x) f 2 (x) • Theantiderivativeoff ′ (x)ef (x) isef (x) + C • Theantiderivativeoff ′ (x)cos[f (x)]issin[f (x)]+C • Theantiderivativeoff ′ (x)sin[f (x)]is− cos[f (x)]+C 2

Antiderivatives Formula Sheet

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