Physical Chemistry Third Edition

1258 C A Short Table of Integrals

∫

xeaxdxeax

(

x

a

−

1

a^2

)

∫

x^2 eaxdxeax

(

x^2

a

−

2 x

a^2

+

2

a^3

)

∫

ln(x)dxxln(x)−x

∫

ln(ax)dxxln(ax)−x

∫

xln(x)dx

x^2

2

ln(x)−

x^2

4

C.2 Definite Integrals

∫π

0

sin(mx)sin(nx)dx

⎧

⎨

⎩

π

2

if mn

0ifmn

(mandnintegers)

∫π

0

cos(mx)cos(nx)dx

⎧

⎨

⎩

π

2

if mn

0ifmn

(mandnintegers)

∫π

0

sin(mx)cos(nx)dx

⎧

⎪⎪

⎪⎨

⎪⎪

⎪⎩

0ifmn

0ifmn(m+neven)

2 m

m^2 −n^2

ifmn(m+nodd)

∫∞

0

e−axdx

1

a

, a> 0

∫∞

0

xne−axdx

1

an+^1

n! a>0,n0, 1, 2,...

∫∞

0

e−ax

2

dx

1

2

√

π

a

, a> 0

∫∞

0

xe−ax

2

dx

1

2 a

, a> 0