"u" the Man!
Partially Correct
Spare Parts
Not Always Proper
Gettin' Triggy With It
Mixed Bag
100
int sin(3x)dx=
1/3 cos (3x)+C
100
Solve for A:
int6/((x-2)(x+1))dx=int(A/(x-2)+B/(x+1))dx
2
100
Identify u and dv. Do NOT integrate.
int xe^(2x)dx
u=x and dv=e^(2x)
100
int_1^oo 1/x^2dx=
1
100
intsinx cosxdx=
1/2sin^2x+C
100
int_0^8 f(x)dx=
11.5 or 23/2
200
int1/(2-3x)dx=
-1/3lnabs(2-3x)+C
200
Find A + B:
int(4x)/((x+3)(x-1))dx=int(A/(x+3)+B/(x-1))dx
4
200
int x cos(x)dx=
x sin x+cos x+C
200
int_1^oo 3/root3 xdx=
diverges
200
int1/(9+x^2)dx=
1/3arctan(x/3)+C
200
int_0^3 f'(x)dx=
[[x,0,1,3],[f(x),4,-3,1],[f'(x),7,2,-5]]
-3
300
inte^(4x)dx=
1/4e^(4x)+C
300
int1/((x-1)(x+1))dx=
1/2ln(x-1)-1/2ln(x+1)+C
300
int x^2e^xdx=
x^2e^x-2xe^x+2e^x+C
300
int_-1^1 1/xdx=
diverges
300
intsec^2x/(tanx)dx=
lnabs(tanx)+C
300
int_5^8 (2f(x)+1)dx=
0
400
intf'(g(2x))g'(2x)dx=
1/2f(g(2x))+C
400
int(5-x)/(2x^2+x-1)dx=
3/2lnabs(2x-1)-2lnabs(x+1)+C
400
intlnxdx
xlnx-x+C
400
int_0^oo 1/(x^2+1)dx=
pi/2
400
inttan(2x)dx=
-1/2lnabs(cos2x)+C
400
int_1^2 f'(2x)dx=
[[x,1,2,4],[f(x),2,-4,14],[f'(x),5,2,3]]
9
500
int(f'(x))/(f(x))dx=
lnabs(f(x))+C
500
int_0^1 3/(2x^2+5x+2)dx=
ln2
500
int e^x sin x dx=
1/2e^x(sin x-cos x)+C
500
int_0^oo e^(-x)dx=
1
500
intcosx/sqrt(sinx)dx=
2sqrtsinx+C
500
int_0^oo x^2e^(-x)dx=
2