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Integrate
int xe^(4x) dx
Integrate
int 1/sqrt(x^2-25) dx
ln|x/5 - sqrt(x^2-25)/5| + C
Integrate
int cos^5(x) sin(x) dx
-cos^6(x)/6 + C
Determine whether the integral converges or diverges. If it converges evaluate it.
int from 2 to infinity 1/x^3 dx
Converges. 1/8
Use the Trapezoidal Rule to approximate the value of
integral from 0 to 2 of x^2 dx
with n = 4.
deltax = 1/2
1/2/2(0^2 + 2*(1/2)^2 + 2*(1)^2 + 2*(3/2)^2 + 2^2) = 2.75
Integrate
int from 0 to pi/4 x*cos(2x) dx
1/2 * xsin(2x)+1/4*cos(2x) eval from 0 to pi/4
= pi/8 - 1/4
Integrate
int sqrt(x^2-9)/x dx
sqrt(x^2-9) - 3 arccos(3/x) + C
Integrate
int cos^2(3x) dx
1/2x + 1/12*sin(6x) + C
Determine whether the integral converges or diverges. If it converges evaluate it.
int from 2 to infinity 4/x^(1/4) dx
Diverges.
Integrate:
int (x-8)/(x^2-x-6) dx
-ln|x-3| + 2*ln|x+2| + C
integrate
int (x+2)e^(2x+1) dx1/2(x+2)e^(2x+1) - 1/4e^(2x+1) + C
Integrate
int from 0 to 3 sqrt(9-x^2) dx
1/2(x*sqrt(9-x^2) + 9 arcsin(x/3))
1/2(9*pi/2) = 9pi/4
Integrate
int sec^4(x) dx
1/3*tan^3(x) + tan(x) + C
Determine whether the integral converges or diverges. If it converges evaluate it.
int from 0 to 5 10/x dx
Diverges.
Use Simpson's Rule with n=4 to approximate:
int from 3 to 4 of 1/(x-2) dx
Round to 4 decimal places.
0.6933
x^2sin(x) -2 sin(x) +2x*cos(x) + C
Determine whether the integral converges or diverges. If it converges evaluate it.
int from -infinity to 0 x*e^(4x) dx
-1/16
Integrate:
int (4x-2)/[3(x-1)^2] dx
4/3ln|x-1| - 2/[3(x-1)] + C