Evaluate the following integrals: `int5^(5^(5^(x)))*5^(5^(x))*5^(x)dx`

1.	Evaluate the following integrals: `int5^(5^(5^(x)))5^(5^(x))5^(x)dx`
Answer» Correct Answer - `(5^(5^(5^(x))))/((log5)^(3))+C` Putting `5^(x)=thArr5^(x)log5dx=dthArr5^(x)dx=(1)/(log5)dt`. `:.I=int5^(5^t)5^(t)(1)/(log5)dt=int5^(u)*(1)/((log5)^(2))"du, where "5^(t)=uhArr5^(t)log5dt=du` `=int(1)/((log5)^(3))"du, where "5^(u)=vhArr5^(u)log5du=dv` `(v)/((log5)^(3))+C(5^(u))/((log5)^(3))+C=(5^(5^(t)))/((log5)^(3))+C=(5^(5^(5^(x))))/((log5)^(3))+C`.

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