Calculus 101

Integrals

100

∫12dy

12y + c

200

∫6x⁵−18x²+7dx

x⁶−6x³+7x+c

300

∫1/x²dx

-1/x + c

400

∫x³(2x+(1/x))dx

((2x⁵)/5)+((x³)/3)+c

500

∫7sin(x)dx

-7cos(x)+c

Limits

100

lim x->10  x/2

5

200

lim x->2   (x²-4)

0

300

lim x->2 (8−3x+12x²)

50

400

lim x->-5 (x²-25)/(x²+2x-15)

5/4

500

lim x->2  (x²+4x-12)/|x-2|

8

Derivatives

100

f(x)= 2x

2

200

f(x)=6x³−9x+4

18x²-9

300

g(z)=4z⁷−3z^-7+9z

g′(z)=28z⁶+21z^-8+9

400

f(t)=(4/t)−(1/6t³)+(8/t⁵)

(−4t⁻²)+((1/2)t⁻⁴)−40t⁻⁶
   

500

z=x(3x²-9)

dz/dx=9x²−9

Anti-derivatives

100

 ∫15x⁴ dx

3x⁵ + c

200

 ∫-3x² dx

-x³ + c

300

 ∫2/x² dx

-1/x² + c

400

 ∫cot x (sin x) dx

( sin x) + c

500

 ∫(7x+8)³ dx

(1/28)(7x+8)³ + c