calc 2 exam

∫sec(x)dx

ln|sec(x) + tan(x)| + C

∫tan(x)dx

-ln|cos(x)| + C.

∫cos(x)dx

sin(x) + C.

∫csc(x)dx

-ln|csc(x) + cot(x)| + C

∫cot(x)dx

-ln|sin(x)| + C

∫sec(x)dx

ln|sec(x) + tan(x)| + C.

backwards power rule

add to power, divide x^n by power number

backwards power rule on fractions

add one, multiply by reciprocal

sqrt(a²-x²)

x=asin(theta)

a²+x²

x=atan(theta)

sqrt(x²-a²)

x=asec(theta)

1+tan²

sec(theta)

after substituting,

use triangle to go to the original variable

USUB step 1

find equation for u (normally under something)

USUB step 2

find derivative of U

∫du/u

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ln|u|+C

PFD linear factors

each part of power gets its own letter if it is a linear factor

PFD irreducible factors

each part of power gets two letters: (x²+9)=A1+A2, (x²+9)²=B1+B2

converges

When given number is bigger than one

diverges

when given number is smaller or equal to 1

ln(x)

1/x