Question

Integrate with respect to 'u'.
x to the power u

Answer 1

it is. indirect method or long method
$let \: y = { x }^{u} \\ take \: log \: \\ logy = u log(x) \\ differentiate \\ (1 \div y)(dy \div dx) = u(1 \div x) \\ (dy \div dx) = (u \div x)( {x}^{u} ) \\ dy \div dx = u {x}^{u - 1}$
another short method is... I. e. direct formula
$generally \: \\ if \: y = {x}^{a} \\ then \: \\ (dy \div dx) = a {x}^{a - 1} \\ here \: it \: is \: y = {x}^{u} \\ dy \div dx = u {x}^{u - 1}$
mark as brainliest if helped
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your answer is as follows
y=x^u
take log
log y=u logx
differentiate
(1/y)(dy/du) =(logx)
(dy/du)=x^u(logx)