Integrals of Trigonometric Functions

∫sinx dx=−cosx

∫cosx dx=sinx

∫sin2x dx=x2−14sin(2x)

∫cos2x dx=x2+14sin(2x)

∫sin3x dx=13cos3x−cosx

∫cos3x dx=sinx−13sin3x

∫dxsinx=ln∣∣tanx2∣∣

∫dxcosx=ln∣∣∣tan(x2+π4)∣∣∣

∫dxsin2x=−cotx

∫dxcos2x=tanx

∫dxsin3x=−cosx2⋅sin2x+12ln∣∣tanx2∣∣

∫dxcos3x=sinx2⋅cos2x+12ln∣∣∣tan(x2+π2)∣∣∣

∫sinx⋅cosxdx=−14cos(2x)

∫sin2x⋅cosxdx=13sin3x

∫sinx⋅cos2xdx=−13cos3x

∫sin2x⋅cos2xdx=x8−132sin(4x)

∫tanx dx=−ln|cosx|

∫sinxcos2xdx=1cosx

∫sin2xcosxdx=ln∣∣∣tan(x2+π4)∣∣∣−sinx

∫tan2x dx=tanx−x

∫cotx dx=ln|sinx|

∫cosxsin2xdx=−1sinx

∫cos2xsinxdx=ln∣∣tanx2∣∣+cosx

∫cot2x dx=−cotx−x

∫dxsinx⋅cosx=ln|tanx|

∫dxsin2x⋅cosx=−1sinx+ln∣∣∣tan(x2+π4)∣∣∣

∫dxsinx⋅cos2x=1cosx+ln∣∣tanx2∣∣

∫dxsin2x⋅cos2x=tanx−cotx

∫sin(mx)⋅sin(nx) dx=−sin(m+n)x2(m+n)+sin(m−n)x2(m−n),m2≠n2

∫sin(mx)⋅cos(nx) dx=−cos(m+n)x2(m+n)−cos(m−n)x2(m−n),m2≠n2

∫cos(mx)⋅cos(nx) dx=sin(m+n)x2(m+n)+sin(m−n)x2(m−n),m2≠n2

∫sinx⋅cosnx dx=sinn+1xn+1

∫sinnx⋅cosx dx=sinn+1xn+1

∫arcsinx dx=x⋅arcsinx+1−x2−−−−−√

∫arccosx dx=x⋅arccosx−1−x2−−−−−√

∫arctanx dx=x⋅arctanx−12ln(1+x2)

∫arccotx dx=x⋅arccotx+12ln(1+x2)