STANDARD INTEGRALS

n

xdx 1 dx ax edx

=

1n+1

x , n ≠ 1; x ≠0, if n <0n +1

=ln x, x >0

1ax= e , a ≠0 1

= sinax, a ≠01

= cosax, a ≠0

1

= tanax, a ≠0

cosax dx

sin ax dx

2

sec ax dx

1 secax tanax dx = secax, a ≠0

1

dx 22 a +x 1

dx

2 a x 2 1

dx

x2 a2

dx 1 x

= tan 1, a ≠0 1 x =sin , a >0, a <x <a

2

=lnx + x 2 a , x >a>0

((

) )

2=lnx + x 2+a

NOTE : ln x =loge x , x >0