What is the integral of cos cube root x dx??

Experts, I'm getting to you for the 2nd time.......plzz Reply!!

Dear Student,
Please find below the solution to the asked query:

I=cos x13dxLet x=u3dx=3u2duI=3sinu.u2duUsing integration by parts we get,I=3u2sinu.du-dduu2sinu.dudu=3-u2.cosu+2u.cosudu=3-u2.cosu+2u.cosuduAgain using integration by parts we get,I=3-u2.cosu+2u.cosu.du-ddu.ucosu.dudu=3-u2.cosu+2u.sinu-sinu.du=3-u2.cosu+2u.sinu+cosu+CI=-3u2.cosu+6usinu+6cosu+CAs x=u3cos x13dx=-3x23.cosx13+6x13.sinx13+6cosx13+C

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