University:
Indiana Institute of Technology
Course:
MA 1200 | Calculus I
Academic year:

2023
Views:

308

Pages:

1
Author:

Katie Dominguez

Calculus - Antiderivative Rules In the rules given below, a 6= 0, k and n are real constants. General Rules Z Z c f (x) dx = c f (x) dx Z f (x) ± g( x) d x = 1 Z f (x) dx ± Z Z k dx = kx + C Z x n dx = Z 1 dx = ln | x| + C x Z 1 1 dx = ln |ax + b| + C a ax + b n+1 x n+1 + C, g(x) d x for n 6= −1 Antiderivatives of Trigonometric Functions Z Z 1 1 cos( ax ) dx = sin(ax) + C sin(ax) d x = − cos(ax) + C a a Z Z 1 1 csc2 (ax) dx = − cot(ax) + C sec2 (ax) dx = tan(ax) + C a a Z Z 1 1 csc( ax ) cot(ax) d x = − csc(ax) + C sec(ax) tan( ax) dx = sec(ax) + C a a Other Antiderivatives Z 1 e ax dx = e ax + C a Z ³ x´ 1 1 dx = tan−1 +C a2 + x2 a a Z Z p 1 a2 − x2 dx = sin−1 ³ x´ a +C ¯x¯ 1 1 ¯ ¯ dx = sec−1 ¯ ¯ + C p 2 2 a a x x −a

Calculus Anti Derivative Rules

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