That was easy
Integrate
\int(4x^2+x+3) dx
What is
4/3x^3+x^2/2+3x+C
Use the Fundamental Theorem of Calculus to evaluate
∫_0^8(3+x)dx
What is 56
Integrate
∫x^2/(sqrt(x^3+3))dx
What is
2/3 sqrt(x^3+3)+C
Use the Fundamental Theorem of Calculus to evaluate
∫_{-pi/4}^{pi/4}sec^2(x) dx
What is 2
Find f(x) given
f^\prime(x) = 3x^2 + 2x + 1, f(2) = 15
What is
x^3 + x^2+x+1
Integrate
∫(2x - 9 sin(x) )dx
What is
x^2 + 9cos(x)+C
Use the Fundamental Theorem of Calculus to evaluate
∫_-1^1(4x^3-2x)dx
What is 0
Integrate
∫x(1-3x^2)^4dx
What is
-(1-3x^2)^5 /30+C
Use the Fundamental Theorem of Calculus to evaluate
∫_0^picos(x/2)dx
What is 2
Given
f^\prime(x) = 12x^2+6x-4, f(1)=1
Find f(x).
What is
4x^3 + 3x^2-4x-2
Integrate
∫(t + cos(t) )dt
What is
t^2/2 + sin(t) + C
Use the Fundamental Theorem of Calculus to evaluate
∫_4^9x\sqrt{x}
What is
422/5
Integrate
∫(sinx)^3cosxdx
What is
(sinx)^4/4+C
Use the Fundamental Theorem of Calculus to evaluate
∫_{-pi/4}^{pi/4}sin(2x)dx
What is 0
Integrate
∫xsqrt(x+5) dx
What is
(2/5)(x+5)^(5/2)-(10/3)(x+5)^(3/2)+C
Integrate
∫10/x^2 dx
What is
-10/x + C
Use the Fundamental Theorem of Calculus to evaluate
∫_1^6 6/x^2 dx
What is 5
Integrate
∫sin(x)/cos^2(x) dx
What is
sec(x)+C
Integrate
∫cos(x)sin(sin(x))dx
What is
-cos(sin(x))+C
Using the limit definition, integrate
∫_0^3(8-2x)dx
What is 15
Integrate
∫1/\sqrt{x^3} dx
What is
-2/\sqrt{x} + C
Use the Fundamental Theorem of Calculus to evaluate
\int_-2^1 x(x^2-6)dx
What is
21/4
Integrate
∫x\sqrt{9-x^2}dx
What is
2/3\sqrt((9-x^2)^3)+C
Integrate
∫x^3/(sqrt(1-x^4))dx
What is
-{sqrt(1-x^4)}/2 + C
Using the limit definition, integrate
∫_2^1(5-x^2)dx
What is 12