How to find the integral of ∫sin3xdx ?

Anabella Gilbert

Anabella Gilbert

Answered

2022-12-23

How to find the integral of sin3xdx ?

Answer & Explanation

Raymond Patel

Raymond Patel

Expert

2022-12-24Added 7 answers

sin3xdx=sinx(1-cos2x)dxsin2x=1-cos2xsin3xdx=sinxdx-sinx.cos2xdx
Solve the first integral.
sinxdx=cosx+C
Solve the second integral.
Let's suppose cosx=u
hence, -sinxdx=du
replace the value,
-sinx.cos2xdx=u2du-sinx.cos2xdx=u33+C-sinx.cos2xdx=13cos3x+C
Combining the aforementioned,sin3xdx=cosx+13cos3x+C
Therefore the required value of sin3xdx is cosx+13cos3x+C

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