Indefinite Integrals

Power rule

100

int 2sqrtx\ dx

3x^2/3 + C

200

int 3x-2 \ dx

3/2x²-2x+C

300

int 2x^(1/2)-4x+2 \ dx

4/3x^3/2-2x²+2x+C

Trig

100

int sinx \ dx

-cosx+C

200

int 2cosx-3sec^(2)x \ dx

2sinx-3tanx+C

300

int (2sinx)/(cos^(2)x) \ dx

2secx+C

Diff Eq's

100

(dy)/(dx)=4csc^(2)x

-4cotx+C

200

(dy)/(dx)=2/3 x^(1/2)-2

y(1)=2

y=(4/9)x^3/2-2x+(2-4/9+2)

300

dy/dx=8x^(1/3)-(1)/(x^(2))

y(1)=0

y=6x^4/3+x^-1-7

How good are you?

100

int (2x^(2)+x)/(3x) \ dx

y=1/3x²+1/3x+C

200

int (4-3x)^(2) \ dx

y=16x-12x²+3x³+C

300

+1 if you answer correctly

Newton

A father of Calculus