Show:
Integrals
Which rule/theorem?
derivatives
anti-derivatives
limits
100

int 3 dx

3x+C

100

ddx x^n=nx^n-1

power rule

100

5x

5

100

12x

6x^2+C

100

lim x approaches 1 (4x+2)

6

200

int 4x dx

2x^2+C

200

ddx f(x)/g(x)=f'(x)g(x)-g'(x)f(x)/G=g(x)^2

quotient rule

200

4x^3+12

12x^2

200

5x^3

5/4x^4+C

200

lim x approaches 2 (3/2x)

3/4
300

int 0 to 1 sqrt(x)+4 dx

14/3

300

ddx f(g(x))=f'(g(x)) g'(x)

chain rule

300

(3x-6)^2

18x-36

300

(2x+10)^2

1/6(2x+10)^3+C

300

lim x approach 0 cos(2x)+5

6

400

int 0 to pi (sinx+1)^2

3pi/2+4

400

integral a to b f(x) dx= F(b)-F(a)

First fundamental Theorem of calculus

400

ddx sqrt(x+12)/x^3

-5x+72/2x^4sqrt(x+12)

400

3x^3+2x^2+11x

3/4x^4+2/3x^3+11/2x^2+C

400

lim as x approach infinity sqrtx-5+3x^2

infinity

500

int 3 to 5 1/(x^2+3x)

-ln(8)-ln(6)-ln(5)+ln(3)/3

500

f'(c)=f(b)-f(a)/b-a

Mean Value Theorem

500

sin (sqrt( e^x)/2)

(e^x/2cos((e^x/2)/2))/4

500

(4ex+3)^2+sinx

1/12e(4ex+3)^3-cos(x)+C

500

lim x approach2 (sin(x^2)/csc12x^2

sin4/csc48