I want to calculate the antiderivative of this

Angelina Proctor

Angelina Proctor

Answered question

2022-04-06

I want to calculate the antiderivative of this function .
f(x)=sinxsin3x1sin3xdx
let sinxsin3x=sinx|cosx| then I have :
sinx|cosx|1sin3xdx , then Assume cosx>0 and if i take t=sinx and then using inverse function of sin it will be complicated , then is there any simple method to Evaluate it ?

Answer & Explanation

szkliwiakinrd

szkliwiakinrd

Beginner2022-04-07Added 10 answers

As you pointed out
sinxsin3x1sin3xdx
=sinx(1sin2x)1sin3xdx
=sinxcos(x)1sin3xdx
Let u=sin(x), then we get
=udu1u3=23sin1(u32)+C

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