or

ask mattrab Visit www.askmattrab.com for more academic resources.

Antiderivatives (Standard integrals)

St

Standard integrals (I)

dxa2x2=12alog(a+xax) + C

dxx2a2=12alog(xaa+x) + C

dxx2+a2=1atan1xa + C

dxa2x2=sin1xa + C

dxx2a2=log(x+x2a2)+ C

dxx2+a2=log(x+x2+a2) + C


Standard integrals (II)

Formula for Integration by parts

 ∫ (uv) dx = u∫ vdx- ∫ (dudx)vdx

∫ eax cosbxdx=eax (acosbx+bsinbx)a2+b2

∫ eax sinbxdx=eax 


Standard integral of trigonometrical functions:


Integral of hyperbolic function:

∫sinhx dx = coshx+ c

∫ coshx dx = sinhx+ c

∫tanhx dx = ln(coshx )+ c

∫ cotdx = ln|sinhx|+ c

∫ sechx dx= tan-1 |sinhx|+c

∫ cosechx dx= ln |tanx2 |+c

Standard integral (III)

dxasinx+bcosx


    =