Why is this true? \int \frac{du}{\tan u \cos^2 u}=\int \frac{d(\tan

Carly Shannon

Carly Shannon

Answered question

2022-01-24

Why is this true? dutanucos2u=d(tanu)tanu

Answer & Explanation

primenamaqm

primenamaqm

Beginner2022-01-25Added 12 answers

d(tan(u))du=sec2(u)=1cos2u
But if you don’t know that derivative, use
tan(u)=sinucosu
take the derivative of that fraction, and use
sin2+cos2=1
ul2ph3ojc

ul2ph3ojc

Beginner2022-01-26Added 12 answers

Because the first integral dutanucos2u is equal to log(tan(x))+C and in the second integral d(tanu)tanu we have that d(tanu)tanu is exactly the closed differential form d(log(tan(u)) (as say dF=F+Constante)

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