An integral giving the area between y=x^2 and y=-3x + 4.
What is the integral (x^2 + 3x - 4) dx from x=-4 to x=1.
100
The antiderivative of 1/(x-3)
What is ln|x-3|+C?
100
The integral of 9x/(16+x^4) dx
What is 9/8[arctan(x^2/4)]+C?
100
The integral of 1/(x^2-4) from x=0 to x=2.
What is diverges as x=2?
100
The integral of x ln(2x).
What is -x^2/4 + x^2/2 ln(2x) + C?
200
An integral giving the volume of a sphere of radius R.
What is integral Pi * (R^2 - z^2) dz from z=-R to R?
200
The anti-derivative of 1/(1+x^2)
What is arctan(x)+C?
200
The integral tan^3(x)sec^2(x) dx
What is (1/4)tan^4(x)+C?
200
The integral of e^sin(x) from x=0 to x=infinity.
What is diverges?
200
The integral of 4xsin(3x) dx
What is 4x*-(1/3)cos(3x)+4*(1/9)sin(3x)+C?
300
The integral giving the volume of the surface of rotation obtained from rotating the region between y=cos(x), y=0, x=-Pi/2, x=Pi/2, about the x-axis.
What is the integral Pi * cos^2(x) dx from x=-Pi/2 to x=Pi/2?
300
The antiderivative of 1/(x^2-4)
What is 1/4 ln|x-2| - 1/4 ln|x+2|+C?
300
The integral cos(x)/(25+sin^2(x)) dx
What is (1/5)arctan(sin(x)/5)+C?
300
The integral of cos^2(x)/x^2 from x=1 to x=infinity.
What is converges by the comparison test?
300
The integral of 4ln(3x) dx from x=1/3 to x=1.
What is 4ln(3) -8/3?
400
The integral giving the surface area of the solid of rotation obtained by rotating the region between y=cos(x); y=0; x=-Pi/2, and x=Pi/2 about the x-axis.
What is the integral 2*Pi*cos(x) dx from x=-Pi/2 to x=Pi/2.
400
The antiderivative of 1/(x^4 +2 x^3).
What is -1/(4x^2) + 1/(4x) + ln|x|/8 - 1/8 ln|2+x| + C?
400
The antiderivative of cos(3x) cos(2x)
What is Sin(x)/2 + 1/10 Sin(5x)?
400
The integral of x e^{-x^2} from x=1 to x=infinity?
What is 1/(2e)?
400
The antiderivative of x^n e^x
What is sum (-1)^k n!/(n-k)! x^(n-k) e^x from k=0 to n?
500
The volume of the solid of rotation formed by taking the region between y=x + 4 and y=4, x=0, and x=1 about the x-axis.
What is Pi*13/3?
500
The anti-derivative of e^{3x} / (1 - e^{2x})
What is -e^x - 1/2 ln| 1 - e^x| + 1/2 ln|1 + e^x| + C?
500
The integral of sin^2(x)cos^3(x) dx
What is (1/3)sin^3(x)-(1/5)sin^5(x)+C?
500
The integral of 1/x - 1/(1+x) from x=1 to x=infinity.
What is ln(2)?
500
Note that f(x) - f(0) = - integral f'(x-t) dt from t=0 to t=x, if we apply integration by parts repeatedly, assuming f has all the derivatives we want, we will derive this.