Physical Chemistry Third Edition

C. A Short Table of Integrals

C.1 Indefinite Integrals

∫

sin^2 (x)dx

x

2

−

sin(2x)

4

∫

cos^2 (x)dx

x

2

+

sin(2x)

4

∫

cosn(x)sin(x)dx

− 1

n+ 1

cosn+^1 (x) n1, 2,...

∫

sinn(x)cos(x)dx

1

n+ 1

sinn+^1 (x) n1, 2,...

∫

xsin(x)dxsin(x)−xcos(x)

∫

xsin^2 (x)dx

x^2

4

−

xsin(2x)

4

−

cos(2x)

8

∫

x^2 sin(x)dx 2 xsin(x)−(x^2 −2)cos(x)

∫

xcos^2 (x)dx

x^2

4

+

xsin(2x)

4

+

cos(2x)

8

∫

x^2 sin^2 (x)dx

x^3

6

−

(

x^2

4

−

1

8

)

sin(2x)−

xcos(2x)

4

∫

eaxdx

1

a

eax

∫

axdx

ax

ln(a)

1257