Calc 2 Chap 1.1 Formulas/ Processes to Memorize

1.1

(power rule)

∫xⁿdx

((xⁿ⁺¹)/(n+1))+C , x≠-1

∫(1/x)dx

ln⏐x⏐+c

∫e^xdx

e^x+C

∫sinxdx

-cox(x)+C

∫co(x)dx

sin(x)+C

∫(1/1+x²)dx

tan^-1(x)+C

∫sec²(x)dx

tan(x)+C

∫sec(x)tan(x)dx

sec(x)+C

∫{1/√(1-x²)}dx

sin^-1x+C

∫e^axdx

(1/a)e^ax+C

∫cox(ax)dx

(1/a)sin(ax)+C

∫sin(ax)dx

(1/a){-cos(ax)"}+C

Chain Rule

d/dx(f(g(x))

f’(g(x))*g’(x)

Steps to Substitution

1. look for the inside function (u)

2. Calculate du=(du/dx)dx

3. convert to an interval of u

4. integrate with respect to u

5. re write with respect to x

∫{1/(x²+a²)}dx

(1/a)tan^-1(x/a)+C

Product Rule

(d/dx){f(x)g(x)}

f(x)g’(x)+g(x)f’(x)

Integration by Parts formula

Let u = f(x), v=g(x)

∫udv=uv-∫vdu

How to get from the product rule to integration by parts

LIATE

a method for finding “u” in integration by parts, go in order

Log

Inverse Trig

Algebraic (x³,5x+x,√x)

Trig

Exponential (e^x, 5^x, lnx)