Integrals

Which of the following statements about the constant of integration is correct?

1. It is added only for definite integrals
2. It is added only when the integral contains x squared
3. It is added for every indefinite integral
4. It is optional

The integral of (f(x) + g(x)) dx is equal to

1. integral of f(x)dx times integral of g(x)dx
2. integral of f(x)dx + integral of g(x)dx
3. integral of f(x)dx - integral of g(x)dx
4. None of these

Evaluate the integral of dx/(x + 2)

1. ln|x| + C
2. ln|x + 2| + C
3. 1/(x + 2) + C
4. x/(x + 2) + C

Evaluate the integral of ln x dx

1. x ln x + C
2. x ln x - x + C
3. ln squared x + C
4. x squared ln x + C

Evaluate the integral of x times e^x dx

1. xe^x + C
2. e^x(x - 1) + C
3. e^x(x + 1) + C
4. x squared e^x + C

If d/dx[F(x)] = f(x), then F(x) is called the

1. Derivative of f(x)
2. Integral (antiderivative) of f(x)
3. Limit of f(x)
4. Gradient of f(x)

The integral of 1/(1 + x squared) with respect to x is

1. sin inverse x + C
2. tan inverse x + C
3. ln|x| + C
4. sec inverse x + C

Using substitution, the integral of (2x)(x squared + 1)^5 dx is equal to

1. (x squared + 1)^6/6 + C
2. (x squared + 1)^5/5 + C
3. (x squared + 1)^6 + C
4. x(x squared + 1)^5 + C

Evaluate the integral of sec squared x dx

1. tan x + C
2. sec x + C
3. -cot x + C
4. sin x + C

The value of the integral of e^x dx is

1. e^x + C
2. xe^x + C
3. e^(x+1) + C
4. ln x + C

If F(x) = integral of (2x + 5) dx, then F(x) is

1. x squared + 5x + C
2. 2x squared + 5x + C
3. x squared + 10x + C
4. x squared + 5 + C

The integral of 1/x with respect to x is

1. x squared/2 + C
2. ln|x| + C
3. e^x + C
4. 1/(x squared) + C

The integral of cos x with respect to x is

1. sin x + C
2. -sin x + C
3. tan x + C
4. sec squared x + C

The value of the integral of (3x squared) dx is

1. x cubed + C
2. 3x cubed + C
3. x squared + C
4. 9x + C

The integral of x squared with respect to x is

1. x cubed + C
2. (x cubed/3) + C
3. 2x + C
4. x squared/2 + C