Mathematical Formulas for Industrial and Mechanical Engineering

G

ð

arccos x dx 5 x arccos x 2

ffiffiffiffiffiffiffiffiffiffiffiffiffi

1 2 x

2

p

1 C

G

ð

arctan x dx 5 x arctan x 2

1

2

lnðx

2

1 1Þ1 C

G

ð

arccot x dx 5 x arccot x 1

1

2

lnðx

2

1 1Þ1 C

5.11 Integrals of Hyperbolic Functions

G

ð

sinh x dx 5 cosh x 1 C

G

ð

cosh x dx 5 sinh x 1 C

G

ð

tanh x dx 5 ln cosh x 1 C

G

ð

coth x dx 5 lnjsinh xj1 C

G

ð

sech

2

x dx 5 tanh x 1 C

G

ð

csch

2

x dx 52coth x 1 C

G

ð

sech x tanh x dx 52sech x 1 C

G

ð

csch x coth x dx 52csh x 1 C

5.12 Integrals of Exponential and Logarithmic Functions

G

ð

e

x

dx 5 e

x

1 C

G

ð

a

x

dx 5

a

x

ln a

1 C

G

ð

e

ax

dx 5

e

ax

a

1 C

82 Mathematical Formulas for Industrial and Mechanical Engineering