MATHEMATICAL RELATIONS 841∫
x^2 dx
(a^2 +x^2 )^2=−x
2 (a^2 +x^2 )+1
2 atan−^1x
a
∫
lnxdx=xlnx−x
∫
eaxdx=eax
a,areal or complex
∫
xeaxdx=eax(x
a−1
a^2),areal or complex∫
x^2 eaxdx=eax(
x^2
a−
2 x
a^2+
2
a^3),areal or complex∫
x^3 eaxdx=eax(x^3
a−3 x^2
a^2+6 x
a^3−6
a^4),areal or complex
∫
eaxsin(x) dx=eax
a^2 + 1[asin(x)−cos(x)]
∫
eaxcos(x) dx=eax
a^2 + 1[acos(x)+sin(x)]
∫
cos(x) dx=sin(x);∫
cosax dx=1
asinax
∫
xcos(x) dx=cos(x)+xsin(x)
∫
x^2 cos(x) dx= 2 xcos(x)+(x^2 − 2 )sin(x)
∫
sin(x) dx=−cos(x);∫
sinax dx=−1
acosax
∫
xsin(x) dx= sin(x)−xcos(x)
∫
x^2 sin(x) dx= 2 xsin(x)−(x^2 − 2 )cos(x)∫∞−∞e−a(^2) x (^2) +bx
dx=
√
π
a
eb
(^2) /( 4 a (^2) )
,a> 0
∫∞
0
x^2 e−x
2
dx=
√
π
4
∫∞
0
Sa(x) dx=
∫∞
0
sin(x)
x
dx=
π
2
∫∞
0
Sa^2 (x) dx=
π
2