Integration by substitution

[arctic anchor]

½∫cos(2u)du needs another substitution:
2u=v
2du=dv
du=dv/2
¼∫cos(v)dv=sin(v)/4=sin(2u)/4=sin(2θ²)/4 + C

@dense pagoda

you made an error with the integration of cos(2u) overall

no clue what you did with the last 2 lines

you did sin(2x)=2cosxsinx? why

[obsidian willow]

the 3rd line, should be sin(2u)/4 cuz integral of cos(2u) is (1/2)sin(2u), multiplied by the 1/2 in front of the integral becomes 1/4, not sure what's the point of the last 2 lines tho cuz till the 3rd line is enough

[dense pagoda]

I used the double angle formula to convert into 2sinthetacostheta

@obsidian willow

@arctic anchor

[arctic anchor]

that will make the integral even more complicated, not less

just do a second substitution as I demonstrated

also that's the sin2x double angle

cos2x is cos²x-sin²x

@dense pagoda

[boreal socket]

@dense pagoda

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