Indefinite integrals of trigonometric functions, their powers and their products.
∫sinax dx=−a1cosax+C
∫sin2ax dx=2x−4asin2ax+C
∫sin3ax dx=−4a3cosax+12acos3ax+C
∫sinnax dx=−a1cosax2F1[21,21−n,23,cos2ax]+C
∫cosax dx=a1sinax+C
∫cos2ax dx=2x+4asin2ax+C
∫cos3axdx=4a3sinax+12asin3ax+C
∫cospaxdx=−a(1+p)1cos1+pax×2F1[21+p,21,23+p,cos2ax]+C
∫cosxsinx dx=21sin2x+c1=−21cos2x+c2=−41cos2x+c3+C
∫cosaxsinbx dx=2(a−b)cos[(a−b)x]−2(a+b)cos[(a+b)x]+C,a=b
∫sin2axcosbx dx=−4(2a−b)sin[(2a−b)x]+2bsinbx−4(2a+b)sin[(2a+b)x]+C
∫sin2xcosx dx=31sin3x+C
∫cos2axsinbx dx=4(2a−b)cos[(2a−b)x]−2bcosbx−4(2a+b)cos[(2a+b)x]+C
∫cos2axsinax dx=−3a1cos3ax+C
∫sin2axcos2bxdx=4x−8asin2ax−16(a−b)sin[2(a−b)x]+8bsin2bx−16(a+b)sin[2(a+b)x]+C
∫sin2axcos2ax dx=8x−32asin4ax+C
∫tanax dx=−a1lncosax+C
∫tan2ax dx=−x+a1tanax+C
∫tannax dx=a(1+n)tann+1ax×2F1(2n+1,1,2n+3,−tan2ax)+C
∫tan3axdx=a1lncosax+2a1sec2ax+C
∫secx dx=ln∣secx+tanx∣=2tanh−1(tan2x)+C
∫sec2ax dx=a1tanax+C
∫sec3x dx=21secxtanx+21ln∣secx+tanx∣+C
∫secxtanx dx=secx+C
∫sec2xtanx dx=21sec2x+C
∫secnxtanx dx=n1secnx+C,n=0
∫csc2ax dx=−a1cotax+C
∫csc3x dx=−21cotxcscx+21ln∣cscx−cotx∣+C
∫cscnxcotx dx=−n1cscnx+C,n=0
∫secxcscx dx=ln∣tanx∣+C