from RD sharma....exercise 19.20

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

I=cos3xdxLet x=tx=t2dx=2tdtI=2t.cos3t.dtWe know that cos3A=4cos3A-3cosaAcos3A=14cos3A+3cosAI=2t.14cos3t+3cost.dt=12t.cos3t+3cost.dtUsing integration by part we get,I=12t.cos3t+3cost.dt-ddt.tcos3t+3cost.dtdt=12tsin3t3+3sint-sin3t3+3sintdt+C=12tsin3t3+3sint--cos3t9-3cost+C=12tsin3t3+3sint+cos3t9+3cost+Ccos3xdx=12xsin3x3+3sinx+cos3x9+3cosx+C

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