AP Calculus Integration Review

The integral of $$\tan x$$ is $$-\frac{1}{2} \text{ln}|\text{cos} x| + C$$ .

The integral of $$\frac{1}{x}$$ is $$\text{ln}|x| + C$$ .

The power rule states that $$\frac{d}{dx} x^n = \frac{1}{n+1} x^{n+1} + C$$ for any real number @@n eq -1@@.

The integral of $$x^n$$ is $$\frac{x^{n+1}}{n+1} + C$$ , where @@n eq -1@@.

The integral of $$\frac{1}{x^n}$$ is $$-\frac{1}{(n-1)x^{n-1}} + C$$ for @@n eq 1@@.

The integral of $$\frac{8}{x^3}dx$$ is $$\frac{-4}{x^2} + C$$ .

The integral of $$11\text{cos} x - 7\text{sin} x$$ is $$11\text{sin} x + 7\text{cos} x + C$$ .

The integral of $$8x^{13}dx$$ is $$\frac{4}{7}x^{14} + C$$ .

The integral of $$\frac{2}{x^5}dx$$ is $$-\frac{1}{2x^4} + C$$ .

The integral of $$\frac{3}{4}\text{sec}^2\frac{3}{4}x - \text{sin}\frac{7}{5}x$$ is $$\frac{4}{3}\tan\frac{3}{4}x + \frac{5}{7}\text{cos}\frac{7}{5}x + C$$ .