University:
Whitman College
Course:
MATH-124 | Introduction to Calculus
Academic year:

2023
Views:

393

Pages:

1
Author:

Camron Farmer

Antidifferentiation Practice R We can write the general antiderivative of f (x) as F (x) = f (x) dx (note that there are no upper or lower bounds). Here’s some practice finding antiderivatives. For some problems, we need to use some algebra first. 1 (x2 + x−2 ) dx = x3 − 2x−1 + C 3 Z √ Z √ 3 2 3 2. ( x3 + x2 ) dx = x3/2 + x2/3 dx = x5/2 + x5/3 + C 5 5 1. 3. 4. 5. 6. 7. Z Z Z Z 1 1 x + x2 + 2 + 4 x 3 2 x(x + 1) dx = Z 1 1 dx = x4 + x3 + 2x + ln(x) + C 4 12 1 1 x3 + x dx = x4 + x2 + C 4 2 sin(x) + cos(x) dx = − cos(x) + sin(x) + C Z 8 √ dx = 8 sin−1 (x) + C 2 1−x Z xe + ex dx = 1 e+1 x + ex + C e+1 Z 1 4 − dx = x−2 − 4x−3 dx = −x−1 + 2x−2 + C x2 x3 Z Z √ y−y 1 dy = y −3/2 − dy = −2y −1/2 − ln(y) + C 9. 2 y y 8. 10. Z Z x2 + 1 + 1 1 3 dx = x + x + arctan(x) + C x2 + 1 3 1

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