Exponential
int 3^x dx
What is
3^x/ln 3 + C
int cos(x/2) dx
What is
2 sin(x/2)+C
int 1/x dx
What is ln |x| + C ?
int sec^2 4x dx
What is
1/4 tan 4x + C ?
If v(t) is velocity,
int v(t) dt
What is displacement?
int (1/2)^x dx
What is
(1/2)^x/ln(1/2) + C
int sec 3x tan 3x dx
What is
1/3 sec 3x + C?
int x^pi dx
What is
x^(pi + 1)/(pi + 1) + C ?
int csc^2 4x dx
What is
-1/4 cot 4x + C ?
If v(t) is velocity,
int |v(t)| dt
What is total distance traveled?
int 3^(3x) dx
What is
3^(3x)/(3 ln 3)+ C
int 1/sqrt(1-x^2) dx
What is
sin^(-1)x + C?
int (3x^2)/(x^3+1) dx
What is
ln |x^3+1| + C ?
int 1/(1+x^2) dx
What is
tan^(-1) x + C ?
int_0^5 r(t) dt
r is rate of snowfall (in/hr)
What is "the number of inches of snow that fell in 5 hours" ?
int e^(sin theta) cos theta d theta
What is
e^(sin theta)+C?
int csc x cot x dx
What is -csc x + C ?
int sin^5x cos x dx
What is
1/6 sin^6 x + C ?
int 1/(abs x sqrt(x^2-1)) dx
What is
sec^(-1) x + C ?
1/(5-2) int_2^5 e^x dx
What is the average value of e^x on (2, 5) ?
int 3^(x^2+2x) (x+2) dx
What is
3^(x^2+2x)/(2 ln 3) + C ?
int tan x dx
What is ln |sec x| + C ?
int (3x^2+2x)sin(2x^3+2x^2) dx
What is
-1/2 cos(2x^3+2x^2) + C ?
int sec x dx
What is ln |sec x + tan x| + C ?
int_a^b a(t) dt
a(t) is acceleration
What is "the change in velocity from t=a to t=b" ?