Integrals

Function for f

100

f'(x)=(1/5)x-2 f(10)=-10

f(x)=[(X^2)/10]-2x

200

f'(x)=(2x-3)(2x+3) f(3)=0

f(x)=[(4x^3)/3]-9x-9

300

* f'(x)=3(x^1/2)+3 f(1)=4

f(x)=2(x^3/2)+3x-1

400

f(x)=6x(x-1) f(1)=-1

f(x)=2(x^3)-3(x^2)

500

f(x)=(2-x)/(x^3) x>0 f(2)=3/4

f(x)=[-1/(x^2)]+(1/x)+(1/2)

Trig

100

∫xcos[2(x^2)]dx

1/4sin[2(x^2)]+C

200

∫(e^x)sin(e^x)dx

-cos(e^x)+c

300

∫sec(2x)tan(2x)dx

1/2sec(2x)+C

400

∫[(csc^2)x]/[(cot^3)x]dx

1/2(cot^2)x+C

500

∫tan2xdx

-1/2ln│cos(2x)│+C

Indefinite

100

∫4/xdx

4ln│x│+C

200

∫1/(2x-1)dx

1/2ln│2x-1│+C

300

∫[(x^2)+(2x)+3]/[(x^3)+(3x^2)+(9x)+1)]dx

1/3ln│(x^3)+(3x^2)+(9x)+1│+C

400

∫(x^3)/[(1+(x^4))^(1/3)]

3[(1+(x^4))^(2/3)]/8+C

500

∫[(x^2)+x+1]/(x-1)dx

[(x^2)/2]+2x+3ln│x-1│+C

Definite

100

∫1/xdx [1,2]

0

200

∫[(x^2)+1]dx [-1,3]

40/3

300

∫e^(2x)dx [0,3]

201.214

400

∫(2x+3)^3 dx [0,1]

68

500

∫√(2/x)dx [1,4]

2√8 5.657