What is the integral of cos cube root x??

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

I=cos x13dxLet x=u3dx=3u2duI=3cosu.u2duUsing integration by parts we get,I=3u2cosu.du-dduu2cosu.dudu=3u2.sinu-2u.sinudu=3u2.sinu-2u.sinuduAgain using integration by parts we get,I=3u2sinu+2u.sinu.du-ddu.usinu.dudu=3u2.sinu+2-u.cosu+cosu.du=3u2.sinu+2-u.cosu+sinu+CI=3u2.sinu-6ucosu+6sinu+CAs x=u3cos x13dx=3x23.sinx13-6x13.cosx13+6sinx13+C

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3 sin (x/3)
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