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Advanced Mathematical Formulas (It took a lot of effort)

College high number formulas, review carefully!

Derivative formula:

2

(tgx) secx

(arcsinx)

2

1 x

2

(ctgx) cscx (secx) secx tgx (cscx) cscx ctgx (a) alna (log

ax

x

(arccosx) (arctgx)

11 x

2

1 x

2

x)

1xlna

(arcctgx)

11 x

2

Basic points table:

tgxdx ctgxdx sec axa

lncosx C lnsinx C

cos sin

dx

2

xx

sec csc

2

xdx tgx Cxdx ctgx C

dx

2

2

xdx lnsecx tgx C

cscxdx lncscx ctgx C

dx

2

secx tgxdx cscx ctgxdx a

x

secx C cscx CC

2

2

1a1

arctglnln

xa

CCC

x ax aa xa xxa

dx

a

x

lna

twenty two

2a12a

shxdx chxdx

2

chx C shx C

ln (x

xa) C

2

2

twenty two

ax

2

arcsin C

dxx a

2

2

2

In

sin

02

n

xdx cosxdx

n

n 1naaa

2

In 2

xa) Cx axa C

2

2

2

2

2u1 u

2

2

2

2

2

x2x2x2

xaxaax

2

2

2

2

twenty two

2

2

ln (x lnx arcsin

2

2

C

2

Rational integration of trigonometric functions: sinx

, Cosx 2

1 u1 u

2

, U tg2

x2

, Dx

2du1 u

2