Power Functions
int(6x^2-10x+2)dx
2x^3-5x^2+2x+c
int(3x-1)^3dx
(3x-1)^4/12+c
int2e^(3x)dx
(2e^(3x))/3+c
int9sin(-3x)dx
3cos(-3x)+c
int5/xdx
5 loge lxl + c
int((x^3-2x^2)/x^2)dx
(x^2)/2-2x+c
int(1-5x)^(3/4)dx
(-4(1-5x)^(7/4))/35+c
int9e^(-3x)dx
-3e^(-3x)+c
int-3cos((3x)/2)dx
-2sin((3x)/2)+c
int(-7)/xdx, x>0
-7ln(x)+c
int(x^3-1/sqrtx+4x)dx
x^4/4-2x^(1/2)+2x^2+c
int10/(5x-2)^2dx
-2/(5x-2)+c
int(10e^(-2x)-2e^(-3x)+2x)dx
-5e^(-2x)+(2e^(-3x))/3+x^2+c
int3sin(2x-3)dx
-3/2cos(2x-3)+c
int(4/(2x-1))dx
2 loge l2x-1l + c
int((x^4-2x^2+3)/x^2)dx
(x^3)/3-2x-3/x+c
int7/3(2x-1)^6dx
(2x-1)^7/6+c
int(e^x(2e^(3x)-2))/e^(2x)dx
e^(2x)+2/e^x+c
int(2cos((3x)/2)-3sin(4x))dx
4/3sin((3x)/2)+(3cos(4x))/4+c
int((3x^2+2)/x)dx, x>0
(3x^2)/2+2lnx+c
The velocity of a particle is the rate of change of its position, x, at time t. Determine an expression for the position of a particle at time, t, when:
v=3t^2-4t+18
x=t^3-2t^2+18t+c
Determine the equation of the curve that passes through the point (2,3) and has a gradient given by:
dy/dx=(3x-8)^2
y=1/9(3x-8)^3+3 8/9
Determine the equation of the function that passes through the point (0,3) and has a gradient function of
f'(x)=e^(2x)-1/e^(2x)
f(x)=e^(2x)/2+1/(2e^(2x))+2
Determine the equation of the function that has the gradient function below and passes through the point indicated:
f'(x)=2cos(3x-pi/2) and (pi/2,-1)
f(x)=2/3sin(3x-pi/2)-1
Find the equation of the curve that passes through the point (e,0) and has the gradient function:
f'(x)=2x+7/x, x>0
f(x)=x^2+7ln(x)-e^2-7