Basic Integrals

What is the integral of @@x^n@@ where n is a constant?

• @@rac{x^{n+1}}{n+1} + C@@

• @@rac{x^{n}}{n} + C@@

• @@n imes x^{n-1} + C@@

• @@rac{x^{n+1}}{n} + C@@

What is the constant multiple rule for integration?

• The integral of a constant is the constant times the variable plus C.

• If k is a constant, then the integral of kf(x) is k(integral of f(x)) + C.

• The integral of a function is always zero.

• The integral of a sum is the sum of the integrals.

What is the integral of @@e^x@@?

• @@e^x + C@@

• @@e^x - C@@

• @@rac{1}{e^x} + C@@

• @@rac{d}{dx}(e^x) + C@@

What is the power rule for integration?

• The integral of x^n is \frac{x^{n+1}}{n+1} + C if n ≠ -1

• The integral of x^n is \frac{x^{n-1}}{n-1} + C if n ≠ 1

• The integral of x^n is \frac{x^{n+2}}{n+2} + C if n ≠ -2

• The integral of x^n is \frac{x^{n+1}}{n} + C if n ≠ 0

What is the integral of @@\frac{d}{dx}f(x)@@?

• @@f(x) + C@@

• @@f'(x) + C@@

• @@\frac{d}{dx}f(x) + C@@

• @@\int f(x)dx + C@@

What is the integral of @@\frac{1}{x}@@?

• @@\text{ln}|x| + C@@

• @@\frac{1}{2}x^2 + C@@

• @@x + C@@

• @@\text{ln}(x^2) + C@@