Memorization Aid (Calc)

f(x) = k
1. derivative
2. integral

1. 0

2. kx +C

f(x) = xⁿ
1. derivative:
2. integral:

1. nx^n-1

2. (1/n + 1)x^n+1

f(x) = e^x
1. derivative
2. integral

1. e^x

2. e^x + C

f(x) = a^x
1. derivative
2. integral

1. ln(a)a^x

2. (1/ln(a))a^x + C

f(x) = ln(x)
1. derivative
2. integral

1. 1/x

2. x ln(x) - x + C

f(x) = 1/x
1. derivative
2. integral

1. -1/x²

2. ln|x| + C

f(x) = sin (x)
1. derivative
2. integral

1. cos(x)

2. - cos(x) + C

f(x) = cos (x)
1. derivative
2. integral

1. - sin(x)

2. sin(x) + C

f(x) = tan(x)
1. derivative
2. integral

1. sec(x)²

2. - ln |cos(x)| + C

f(x) = sec(x)
1. derivative
2. integral

1. sec(x)tan(x)

2. ln |sec(x) + tan(x)| + C

f(x) = csc(x)
1. derivative
2. integral

1. - csc(x)cot(x)

2. - ln| csc(x) + cot(x)| + C

f(x) = cot(x)
1. derivative
2. integral

1. - csc(x)²

2. ln | sin(x)| + C

f(x) = arcsin(x)
1. derivative
2. integral

1. 1/sqrt(1-x²)

2. x arcsin(x) + sqrt(1-x²) + C

f(x) = arccos(x)
1. derivative
2. integral

1. -1/sqrt(1-x²)

2. x arccos (x) - sqrt(1-x²) + C

f(x) = arctan(x)
1. derivative
2. integral

1. 1/1+x²

2. x arctan (x) - ½ ln |1+x²| + C

f(x) = arcsec(x)
1. derivative
2. integral

1. 1/ x sqrt(x² - 1)

2. x arcsec (x) - ln |x + sqrt(X² - 1)| + C

f(x) = arccsc(x)
1. derivative
2. integral

1. -1/ x sqrt(x² -1)

2. x arccsc (x) + ln |x + sqrt(x² - 1)| + C

f(x) = arccot(x)
1. derivative
2. integral

1. -1/1+x²

2. x arccot(x) + ½ ln |1+x²| + C

f(x) = arcsin (x/a)
1. derivative

1. 1/ sqrt(a² - x²)

f(x) = 1/a arctan (x/a)
1. derivative

1. 1/ a² + x²

f(x) = 1/a arcsec (x/a)

1. 1/x sqrt(x² - a²)

sin values:
1. 0
2. pi/6
3. pi/4
4. pi/3
5. pi/2

1. 0

2. ½

3. sqrt(2)/2

4. sqrt(3)/2

5. 1

cos trig values:
1. 0
2. pi/6
3. pi/4
4. pi/3
5. pi/2

1. 1

2. sqrt(3)/2

3. sqrt(2)/2

4. ½

5. 0

tan trig values:
1. 0
2. pi/6
3. pi/4
4. pi/3
5. pi/2

1. 0

2. 1/ sqrt(3)

3. 1

4. sqrt(3)

5. undefined

sec trig values:
1. 0
2. pi/6
3. pi/4
4. pi/3
5. pi/2

1. 1

2. 2/sqrt(3)

3. sqrt(2)

4. 2

5. undefined

csc trig values:
1. 0
2. pi/6
3. pi/4
4. pi/3
5. pi/2

1. undefind

2. 2

3. pi/2

4. 2/sqrt(3)

5. 1

cot trig values:
1. 0
2. pi/6
3. pi/4
4. pi/3
5. pi/2

1. undefined

2. sqrt(3)

3. 1

4. 1/sqrt(3)

5. 0