The Chemistry Maths Book, Second Edition

Appendix. Standard integrals

Indefinite Integrals

For simplicity, the constant of integration has been omitted from the tabulation.

(n 1 ≠ 1 −1)

Zcos(ax b dx) sin( )

a

+=ax b+

1

Zcosxdx=sinx

Zsin(ax b dx) cos( )

a

+=−ax b+

1

Zsinxdx=−cosx

Zedx

a

e

ax b++ax b

=

1

Zedx e

xx

=

Zxxdx

x

n

x

n

n

n

ln = ln

• 
  

−

• 
  













+ 1

1

1

1

Z

ln

(ln )

x

x

dx= x

1

2

2

Z

dx

ax b a

ax b

• 
  

=+

1

ln( )

Z

dx

x

dx=lnx

Z()

()

()

ax b dx ()

ax b

an

n

n

n

+=

• 
  

• 
  

≠−

+ 1

1

1

Zxdx

x

n

n

n

n

=

• 
  

≠−

+ 1

1

() 1

Ztan tan

2

xdx=−x x

Zcos ( sin cos )

2

1

2

xdx x=+x x

Zsin ( sin cos )

2

1

2

xdx x=−x x

=

• 
  

• 
  

















e

abxbbx

ab

ax

cos sin

22

Zebxdx

ax

cos

=

−

• 
  

















e

abxbbx

ab

ax

sin cos

22

Zebxdx

ax

sin

Zsec

ln tan

ln

sin

sin

xdx

x

x

x

=

• 
  













• 
  

−







π

42

1

2

1

1













Z

cosecxdx

x

x

x

=

−

• 
  















ln tan

ln

cos

cos

2

1

2

1

1

Zcotxdx=ln sinx

Ztanxdx=−ln cosx